I think one of the main issues with a non CO2 tank is the balance changes a GREAT deal comparatively, vs the CO2 enriched tank with respect to plant biomass.
Now things can progress VERY nicely in lakes, and in tanks without CO2 enrichment. Till you get to a point where the biomass is too unsustainable for the tank.
CO2 enrichment and dosing more, soil based sediments can extend this, but there is a HUGE difference between this tank and the the next shot:
Nothing done to the tank, just let it overgrow:
Now is the nutrient uptake the same for both cases with 2x the plant biomass?
What about all the plant biomass getting shaded and about to rot/decay?
Is the CO2 and O2 demand the same in both cases by the entire aquarium?
Here's a non CO2 example, but the CO2 is not an issue due to the emergent growth, but the nutrient uptake is VERY different.
A few months later:
Now if you have a planted tank that is non CO2, you dose/feed fish as you always do...........no more CO2 is coming in.............and.........typically, not much change in the nutrients, but you have serious changes in the flow in the tank and the CO2 will drop and the plants will strongly and aggressive compete more for CO2.
This EXACT same thing happens to reef folks with refugiums with macro algae, they get let it go and till it basically eats itself out of house and home. Caulerpa will disintegrate and form spores(think algae seeds) when the weather, or in this case, the NO3, drops too low for vegetative growth. So boom and bust.
The spores are far more motile and can hopefully find a better location with NO3 or can simply wait till next season when runoff, upwelling etc bring nutrients and sun to the region.
If you add more CO2 and/or fertilizer, this might not occur, but a more obvious thing and balance: simply trim and hack the plants back, a little bit each week or two.
Do not let it go 3-6 months, then to do a big boom/bust. Trim a little and often, especially the pennywort, that stuff is a weed and will take over.