f you have the salts, then you simply adjust the KNO3 and the KH2PO4, then you get about 15-20ppm NO3 and 3-5 ppm of PO4.
Many do not add much PO4, there is a long stigma about PO4. And if one thing is limited strongly or even moderately, then the others build up more, but water changes prevent much issue there.
Also, a scape does not imply anything about the ferts to the water. A scape is based more on art, less on actual long term routines.
ADA and Tropica soil etc, there's a lot of ferts in there. I see plenty of ADA tanks in bad shape also. You only seem to suggest that the ADA and Elos tanks are always nice, they are not. All methods have issues, the issue is less to do with the methods, rather, the user.
ADA and Elos often sell the entire packages, which means they sell the lights............which are lower power in most cases than most other brands. I've measured a number of these full set ups and have provided the data to support this. That really makes a huge difference. They also suggest redoing the tank every 1-2 years and replacing the soil. This is because the soil runs out of N mostly. It is easier for many hobbyists in that respect, but many hobbyists will no pay the $ for the pricy brands and names, products etc. So ADA cannot be all things to all people, not by a long shot.
I would use H2O2 over Excel or Easy carb also if I needed it.
As far as EI, if you limit something, say PO4 moderately, then the issues with CO2 will go away, because PO4 is a bit more limiting than CO2, and algae responds better to PO4 limitation than CO2 issues. This has been shown for a very long time. But the relationship is indirect, and in accordance with Liebig's law. As we also have nice examples of tanks that operate very well with no issues with high PO4/NO3/Traces etc...and no algae issues of any sort.
This goes back to the lighting, the routine, the aquarist. Not the general ranges of ppm of a nutrient.
Those are relative minor compared to light and CO2. you can vary the ppm's and ratios over a very wid erange without issues for logn time frames....if..the light and CO2 are balanced well. And the lower moderate light with rich CO2 tend to be the most robust of all.
I've had these same conversations for 20+ years.
Example: my 70 Gallon Buce tank, which I dose EI, actually higher, and I have zero such issues with any algae.
Soil will help some as well tannins, and lower the KH some in many cases, that has a strong effect in many cases.
Over time, that effect wears off.
Generally, rich soils will help over time for most aquarist.
But they are not required, but they can add the primary or a good backup for the water column fert sources.
I use both.
Still, a specific goal is not going to have every method equally the same end result.
But..........we can rule out what is not the issue. Then that leaves us with more likely issues, mostly limiting another nutrient, CO2, or light.
Light alone is poorly tested and measured, that leads to all sorts of headaches.
CO2 use, also poorly adjusted and tested. Nutrients are pretty easy on the other hand.
So they tend to be the thing hobbyists blame. Ask Tropica about this. Light(too much) and poor CO2.