Wow FishingBuds, that’s an interesting theory and question. Got me thinking. I’ll do the TL : DR first. Your theory has merit, but it depends on the individual aquarium.
Firstly, the air stone causes surface agitation and what does surface agitation do? The various gases dissolved in the water are trying to achieve equilibrium with the gases in the atmosphere. Surface agitation will assist this process. If levels of any gas are higher than the equilibrium they will offgas into the atmosphere, if lower the water will absorb said gas from the atmosphere.
What I think you are trying to achieve is keeping the CO2 in the water while the plants need it for photosynthesis by reducing surface agitation during the day and then get the O2 levels back up by night when the CO2 isn’t needed. This would be the solution in a high tech system with injected CO2 because the CO2 levels are unnaturally high and will offgas with surface agitation. But, in a low tech tank when CO2 levels are lower, is this necessary?
The processes that produce CO2 in a low tech set up are fish breathing and plant matter decomposing. The negative side of the equation is photosynthesis during the day. If those processes take the CO2 levels above the equilibrium point then surface agitation will cause CO2 to offgas and your theory to only have the airstone on at night when the plants don’t need the CO2 has merit. If however those processes don’t produce CO2 levels above equilibrium, then you would be better having the airstone on 24/7 as it would in those circumstances cause the water to absorb CO2 to the benefit of your plants.
I would suggest that in a highly stocked tank with lots of decaying plant matter (ie lots of CO2 producers) then turning off the air stone during the day might benefit the plants. You would also have to consider whether the plants would then produce enough O2 for the fish. In most low tech set ups however, I don't think the CO2 levels would get above the equilibrium point and benefit from turning off any surface agitation.
