weelllll... While I'm ok with a large tank with tonnes of plants in it and maybe one or two smaller fish having no filter, the filter really is mainly for the fish. Most people put more fish in a fish tank than the plants in the tank can really support (bioload-wise). Like, I am certain that my thirty gallon aquarium with plants would be fine for one betta - but since I put two dwarf gouramis and four female bettas as well as six otos and snails in there...
also, a filter helps to keep the water clear. I know some people are patient enough to wait a month for the sediment to settle in their tanks, but I'm not! If I can have the excess mechanically filtered out through filter floss, I'm all for it.
I think most people here just don't use the carbon filtration, as it leaches all the "good stuff" that plants use out of the water... but of course, there are plenty of people who will vouch for no filtration in heavily planted tanks, but mostly for situations that I described above.
And also, I'm not positive, but I THINK the filter helps turn the ammonia into nitrites and then nitrites into nitrates that the plants can use more readily. I could be very wrong, though.