Many fish can live without a filter, but they are in entirely different circumstances than what we have in a tank.
Nature has a natural filtratrion - flowing streams, evaporation, etc, as well as a biofilter that works constantly. Fish are not concentrated in one place, either - they are spread out quite thinly. When you look in a lake or a stream, you will be lucky to see one or two fish.
Any time you put a high concentration of fish into a "small" water volume, you need to find a way to deal with the fish waste. Nature cannot do it - it is simply too much - besides, your water is not flowing down a stream!
A filter is a mechanical invention to allow us to keep fish in small, attractive water containers in our houses, for our enjoyment.
As I am sure you have read here, the most efficient way to do this is to create a biological filter with beneficial bacteria that your tank water flows through constantly - hense a power filter of some nature.
As Laurie says, other than a filter, you will need to change the water every day. That is a BIG bother. I would rather spend my time enjoying the fish!