There are a couple of possible "advantages", one can be over come as an "advantage" and ends up being a bad idea. The other is a very valid reason for many: simplcity.
Some suggest they cannot get enough CO2 into the water without it running 24/7. It may take 6 hours after the lights are on to play catch up for good CO2 ppms.
But this is not due directly to the method of adding CO2 24/7, it just say that they have a very weak, wimpy , underated, low power CO2 diffusion method.
The faster the response time, the better and more control at adjusting the CO2 ppms for the tank.
That was one of thye main things I suggested when using CO2 mist.
Faster dosing to the plants, faster response times.
ADA disc are used not just in one spot in Amano's tanks, often large tanks have 2 or more disc. Water current runs directly into the mist.
Rather than having a reactor outside the tank, the tank it self/water is the reactor chamber.
My angle was more like: why wait for the gas to dissolve into the water to get it to the plants?
CO2 is less souble in softer water, so it'll have more resistance to being dissolved and will persist longer as a gas. A lot or little more? Probably a little. Not quite sure.
The 24/7 method for simplicity?
that's not a bad idea for DIY users or folks using their filter intakes/filters as CO2 reactors, but...........adding a small powerhead that does the same thing can easily be plugged into a light timer etc so it's not really that less simple, nor is using a solenoid that often come with regulators.
But adding it at night vs these two main arguements vs the fish health and error of adding too much and gassing the fish/shrimps etc is noit worth it for myself.
I'd rather error on their side than to accept that simplicity.
But you can use either method successfully, and to a greater degree in terms of plant growth with the day time only CO2 enrichment, since you do not have much build up from the previous cycle.