I do try to have plants in all my tanks (where they won’t get eaten). No matter what, you need some sort of filter or bubbler to turnover the water and aerate the tank though.
In one of my tanks, the filter is only used for turnover and extra space for bacteria, so I suppose that counts as the plants (or algae) being the main source of filtration for nitrate - must be working for nitrates to always come back undetectable.
This only works in a lightly stocked tank though - plants can only keep up with so much.