I have heard of some people trying a filter less tank. No PH or other pump, no heater. Nothing to provide water movement.
Problems: Most fish die, leaving one hardy species (usually Guppies or Platies) to populate the tank.
With no water changes, just topping off, the GH and KH (and therefore pH) are skyrocketing. The tap watering one case used for top off has more minerals than the plants are using. This happened to my tanks this summer, I was doing fewer water changes and more topping off, and my tap water is not very hard. (KH and GH around 5 degrees)
Answer to original Q: Each person has their own experiences with less than average filtration, even if only by accident, and will have a different answer for you. Filters or powerheads quit, and a tank may need to survive for several hours or a day or so until something can be worked out.
When this sort of problem happens to my tanks the fish are gasping at the surface suggesting that the circulation is providing the required oxygen. Circulation stops, and oxygen levels go down. I have air pumps that I can add immediately, and certainly I look into why the filter or PH has quit (or slowed)
I would not completely remove the filter, or even swap filters (new filter onto established tank, established filter onto new tank) without also removing some of the fish to the new tank. As good a job as the plants are doing at nitrogen removal there is still all the other things that the whole aquarium ecology is dealing with, and removing the well established microorganisms from the filter will disrupt this ecology.
As I noted above: I have had good results removing a maximum of 25% of the media from an established tank's filter. This is enough to jump-start the new tank, and not so much to stress the old tank.