My dad once said that "a rose is a weed in a vegetable garden".
It's all about what you want there. Of part of the problem with plants becoming overgrown is the hyper-eutrophication (from sewage and wastes) of waters near urban centres. Think of it like dumping masses of ferts into your tank and seeing what happens: one of two things, plants choke out everything or algae chokes out everything. It's really just a matter of which wins out, but in either case, the fish lose.
I don't think that there's much danger for me flushing my clippings down the toilet, our wastes flush into the harbour and I doubt that my plants will do well in salt water. Plus winters would kill them off anyway. However, I still don't anymore. I did initially and then started thinking that while it probably won't hurt it's just not good practice.
Not that I think that aquarists are at all to blame for weeds choking waterways, but I think that it's important for us to be responsible with our wastes and as aquarists we have all the more reason to be attentive of the aquatic environment and our impact on them.
But aquariums need plants. If you don't have plants, or at least some aquascaping, it's not an aquarium, just a fish tank.