I have a 5g moss ball tank with only snails and no filter. The snails were stowaways, and have really taken off in there. I have not had any problems with algae either. There is also a clam in there.
That's how tanks used to be done in the late 19th, early 20th centuries.It was feasible also because paradise fish were among the first tropicals kept and, like bettas and gouramis, they're labyrinth fish. Hence they could tolerate more polluted water. (I'm not sure when in the hobby the value of water changes was first known.)
I have two filterless tanks. They are only months old. It will be years before I know if there is an advantage. I don't think the filters do much that a power head does not to be honest.