There's not much reason for people to really grow plants in my opinion. It doesn't do enough to just have your name on something and the age, although it makes it more worth objects that don't. There's not much reason to them. For example: Why would a community want to take care of a plant? The age would matter after time had passed but there wouldn't be anything really of importance other than that, time.
Now, if the plants grew resources or the plants were unique in some way, like if you clicked upon it, maybe you could get some kind of luck boost or strength or maybe if you squeezed a leaf, you could extract color from it or if reagants gave a bonus to damage, you might want to grow reagants. I don't just want to visit my plant every day and watch it grow old knowing that I will die long before it dies or shortly after I die, it will die.
Community gardens I think would be much more popular if the plants did anything else but get old. The nice thing about this type of garden should be that anyone can tend the plant and get resources from it. So, when you plant it, you plant it for everyone. When you take care of it, you take care of it for others. What do others get from your name being on the plant?
House plants should also age. Now this makes more sense because when people come into your house they can see that you're a gardner and by judging by the age of the plant they can tell how much you care about plants. So, it's a way of sharing with people your devotion. When people see a plant now in your house they just think about this lunatic cycle that you must be carrying out endlessly for no reason but that's just my opinion.
If I had my way, all plants in the world would age, whether they were planted by people or not. Maybe there would be some type of Lore Gump for a plant, telling you its' strength, its' resource, its' age, who planted it, when it cycles its' resources.
Then even a tree out in the woods could possibly survive on its' own because then the system would know that it had rained or that the sun was just right for it to grow. There might even be types of animals that live in this type of tree but at least for now we have the plants that we do but I think I have finished my cycling of buying pots and filling them with dirt.