While much of the attention and aquascape seen on the web focuses on CO2 enrichment in their methods, Diana Walstad presents an excellent argument for the approach of a non CO2 enriched planted Aquarium. We should also extend this to include Excel and carbon enrichment liquids as well as acetate which allow some algae to exist without any light or CO2 and grow heterotrophically (like us). She discusses not needing test kits, water changes, pruning often, dosing, work that most aquarist do not care for.

What? You mean no water changes? Yes, that's right.
No testing? Yes, that's right, but you can if you wish.
Not much pruning? Yes, that's right, the plants grow much slower.
No dosing? Generally yes for many easy to care for plant species(I'll discuss this much more later), the fish waste represents the dosing and you feeding them daily adds the nutrients.

So why don't more folks do it?
I'm not sure, given the goals they say they want when setting up a planted tank. Seems like it would be exactly what many claim they seek.
CO2 is a bit like a drug addiction that hobbyists get hooked on. That's fine, but this non CO2 approach will give an excuse to have another tank that needs less attention and is cheap.
I suggest folks coming from either the non CO2 or the CO2 enrichment approaches to give the other method a try and see what benefits it has.

CO2 and non CO2 tanks work for all the same reasons, but........
They grow at different rates.

Based off of my testing, I'd estimate close to 5 to 10 times slower than a CO2 enriched tank at 2-3 w/gal.

This rate of growth is such that the fish waste alone is enough to supply the needs for the plants. If we added more light then the CO2 would start becoming a more limiting factor and allow algae to grow better (algae need higher light to grow well in non CO2 enriched systems wereas the plants are much more limited without CO2). A lower light level is required, generally about 1.5 to 2w/gal is good.

We also need a balanced fish load and feeding routine since this is our main long term input of plant nutrients. Fish food varies in it's amount and ratio of nutrients. This is not an issue unless it becomes limiting. Very often since non CO2 tanks get neglected, they have trouble growing certain plants. If these nutrients are not allowed to bottom out(Say PO4 or NO3), then many of the species folks suggest cannot be kept, suddenly can be kept in non CO2 tanks but they simply grow slower.

Rather than suggesting allelopathy, Fe algae limitation of PO4 limitation, I will say none of this exist. I simply do not see evidence for this in our aquariums, and can test these hypothesis easily(Ask me, I'll show you how). Rather, non limiting nutrient levels for plants will provide better conditions. While nutrients are part of this, CO2 limitation still exist and is why many species cannot grow well in non CO2 planted aquariums. Plants compete with each other very strongly for CO2. Some are obviously much better at acquiring CO2 than other species, this, not nitrogen or potassium limitation is generally the problem for many species. This CO2 competition is very well supported in the research, every weedy aquatic plant is typically very good at acquiring CO2 in a limited competitive system.

They have to be to grow fast and take over a habitat.

CO2 will limit both plants and algae, the lower light and high plant biomass density will provide a better place for the plants and a worse place for the algae. CO2 and non CO2 tanks work well and are algae free namely due to high plant biomass that is relatively healthy. This plant biomass removes NH4 from the fish waste and other nutrients. Some plant species are algae busting, take up nutrients faster etc because they are better than other species at gathering light but mostly due to their rapid CO2 acquisition. This way they can take up the other nutrients if they are well supplied with CO2 and can out compete other plants. algae are not CO2 limited and are very well adapted to aquatic systems with low CO2. So there's no competition for them involved here, many seem to think so, but there's little evidence for it in non CO2 planted tanks(we can add PO4/NO3 to high levels without issues, just like CO2 enriched systems)
We can add KNO3 and KH2PO4 and show that in a non CO2 tank, excess PO4, NO3 (and Fe) do not cause algae blooms. We can add NH4 and induce a bloom just like a CO2 enriched tank. This assumption and knowledge frees us from limitation of nutrients which ultimately does more harm to the plants' health and well being, allowing a better environment for algae to grow.

Doing water changes adds CO2 back to a CO2 limited tank.
Plants and algae both can and do adapt to low CO2 environments and induce genes to make enzymes that concentrate CO2 around Rubisco, the CO2 fixing enzyme. Algae tend to be better at it and have a faster response time and much shorter life cycle. When we add the CO2 at higher levels, this causes the plants and algae to destroy the low CO2 enzymes and start growing without of them since they no longer need them to fix CO2 form the KH ( the -HCO3).
Why keep all this machinery around if you no longer need it? Doing weekly water changes "fools" the plants and helps encourage algae more. Algae are faster to respond to low CO2 than plants.
Once the plants do adapt, they can do well. Plants want stable CO2 and nutrients to do best.

Soil substrates are popular with non CO2 users and they work well but often peter out after about 6-12 months. They help the plants get established initially and supply nutrients that are other wise lacking in the beginning before many fish are added and the tank has had a chance to accumulate waste. There are many variations for soil sediments for non CO2 planted tanks, often leading is a messy disaster for many aquarist. These methods can and do work well, but there are very few "standard soils" so there's a correspondingly wide range of results:) This causes many issues for folks. Mineralizing the sediment for 3-8 weeks prior to use helps, this helps leach the NH4, establish a large bacterial community and reduces the initial O2 demand. The bacteria rapidly start oxidizing the soil and this lowers the O2 level in the tank for the first few weeks. This is similar to a stream, lake, pond having a spring run off with a large amount of organic matter from outside the system suddenly flood the aquatic system. This is a good time for algae to grow if there's also enough light. Plants also respond, but are much slower and demand far more CO2.

The Dry start method works good for non CO2 tanks also for mineralizing sediments, bacterial colonies and establishing good root development.

The method below is a water column alternative to the sediment method and is pretty easy.
I suggest onyx sand as it added Ca, Mg, and Fe, and I add mulm/detritus freshly from another established tank to add bacteria and cycle the tank immediately. I also add a form of organic material other than soil. The bacteria that break the waste down need a source of carbon as an electron donor besides the elements in the waste. Like us, they need their carbs as well. As these bacteria break the carbon and waste down, they consume O2.
This lowers the redox values in the substrate freeing up Fe2+ and other nutrients. Add too much organic matter and O2 and you get O2 levels that are too low and cause issues for your tank. Soil also has NH4, this we know to cause algae in higher amounts and it does not take much! Ways around this: don;t use soil, it's messy and has NH4/urea. Boiling the soil for a few minutes will oxidize the NH4 to NO3. Allowing damp soil to be spread thinly outside for few weeks(3) will allow the NH4 to be converted into NO3 by bacteria. Peat moss, ground peat, works well also. The other options are add lots of mulm instead and leonardite. Leonardite is great, it last a very long time, adds a slow release form of carbon, matches the gravel's color, sinks easily poses no issues if you disturb and uproot plants. You should always add fresh mulm to any new tank. Add some form of carbon as well, pre soaked/boiled soil, pre soaked peat, leonardite.

Since the plants are the same as they are in a CO2 enriched tank and we know the rates of uptake are there, we can scale down the rates for the non CO2 dosing routine. I removed all fish and critters from the test tanks, I dosed only with KNO3m, and other inorganic fertilizer so that I would see only plant uptake and inorganic ferts contributions to the plant's health. Going back and assuming 80-90% of the nutrients will come from the fish load, I added once a week KNO3/KH2PO4. While trace mixes can be added, I decided to use SeaChem Equilibrium instead. It has Fe and Mn as well as Ca/K/Mg/SO4. I will add about 1/4 teaspoon per 20 gal tank once every week or two.
This greatly enhances the growth of the plants. I also will add about 1/8" and 1/32" teaspoon of KNO3 and KH2PO4 respectively once a week or two. Note, GH Booster can be used instead of Seachem Equilibrium
The plants will respond very well to this routine. You can let the tank go for awhile and not dose to purge any excesses that might have built up over a month or two or you can test to see rather than do the water change.

Diana Walstad does not suggest dosing(sediment only), but adding 2-3 things once a week or two, certainly is not that tough???? The plants do gain a lot and then you can grow more species over a longer time frame for nutrient supply in a non CO2 tank.

From here if you want more growth, Excel is a good option. You can add about 2-3x as much ferts then and implement water changes again(Say 1-4x a month, 25-50%).

This should give you enough background to set up such a tank and reduce the rates of growth to a simple amount for most anyone to easily manage.