re-read what you have just written? it doesnt make sense does it?
just having light wont make plants grow happily and healthily. you need nutrients and coo2 to complete the triangle.
you wouldnt say a fire will light with just fuel would you? you need the heat (source of ignition) and the oxygen...
terrestrial plants have access to about 300ppm co2,in our planted tanks we aim for abbout 30ppm which is a safe bet for not gassing the fish. now thats only a tenth of what is accessible if they reach the surface, so by not adding co2, you are going to have around 5-10ppm in your water which is not enough. furthermore, this is going to fluctuate massively, for examplee when you do your water changes, this often co-incides with the photoperiod ruining that particular days growth in essense. fluctating co2 and ferts levels are what causes the algae outbreaks....
its all about achieving the balance, an equilibriium.
yes, light is a factor but most people far over do it with light and experiance all kinds of issues. supercoleys tank is a good example, relatively low light but his plants are growing very nicely, its the perfect low tech set-up. as i said before, you can grow anything under 2 30w t8's, its co2, ferts and also flow many inexperianced planters overlook.