The best I ever did at growing plants was in a 15 gallon tank that I had when I was in my early teens. That tank was probably the prettiest tank I ever had. I had some kind of val, anacharis, pygmy sword plant and hornwort all growing and in some cases reproducing. I think the reason that the plants were doing so well, is that at that time, I didn't understand the concept of periodic water changes. That tank was pretty completely populated, and I am sure there was plenty of fertilizer present after a few months. Eventually as you would expect that tank crashed, and the medicine I put in the tank to help the fish, killed the plants.
When I lived in South Florida, I kept a row of 4, 10 gallon unheated tanks in the screened in porch I had. I tried live plants several times in those tanks. They would grow quite well for a few weeks, and then slowly fade away after that. I suppose they ran out of some vital nutrient after that first period of healthy growth.
Since then, I have tried planting the 55 gallon tank I currently have. Unfortunately in the water I have, it appears that algae grows better and faster. The algae coats and strangles most plants. I do have a tough amazon swordplant of some sort that is somehow hanging on. Also I have plenty of algae coated anacharis that seems to do OK when the PH is below 7.0. I suppose when I solve the algae problem, I could try working in some new plants.
In any case, my experience with growing plants in aquariums is mixed. I think it takes a dedicated aquarium keeper with a big fancy for water plants to consistently succeed.