Your basic concept is quite valid. Plants will indeed remove a lot of the waste from an aquarium.
The most basic concept is ANY sort of circulation, then put plants in the path of that circulation. There are all sorts of ways of setting it up.
In a pond set up I have seen the same idea. It is quite common.
Set up 2 ponds. One is the main pond. The other is more of a shallow stream. Put lots of plants in the shallow stream (in pots or planted directly in the stream). Grow the plants that thrive with their leaves out of the water. Pump the pond water through the stream. Stream is about 10% or more of the volume of the pond.
For aquariums I have seen quite a few ideas.
Planted HOB.
Planted sump. Refugium.
Set up a box above the tank for the plants and pump some aquarium water through that. The box is planted with house plants, vegetables or other plants.
Look up Aquaponics, Hydroponics and related terms. These deal more with growing vegetables, and some incorporate raising food fish with the vegetable gardening.
You can get as complex as you want, or keep it as simple as you want.