Ok at risk of being mauled...
I was given advice that Bettas actually dont like filtered water/moving water, and just to keep on top of water changes. So by that logic a filter isnt overly necessary....
They often dislike MOVING or turbulent water because they are poor swimmers due to their long fins. It also makes building bubblenests very hard as the movement of the water disturbs or breaks up the nest.
FILTERED water is really needed in order to keep a healthy biological cycle. Yes, you can keep up with water changes in order to keep the waste down, and many do that very successfully. But what if you forget ? Or have to go away and leave the fish in the hands of someone who doesn't know what they are doing? You can't possibly predict that you won't forget, or be ill, or will always have a knowledgeable friend.
A filter helps greatly because it does the work for you. The bacteria do the work for you. Using a 5 gal as an example again, I do twice weekly 50% water changes on my mother's tank, and the ammonia and nitrites are always at 0 Nitrate tends to stay at around 15-20 ppm.
Can you garauntee that with an unfiltered tank? Taking into account the fact you may forget or be ill ect and not be able to change the water? No. The filter simply makes everything so much simpler and easier.
As for the flow of water disturbing the fish, small hang on the back filters, and many small internal filters have an adjustable flow rate , or can be modified with a piece of plastic to slow down the flow if they do not. Sponge filters are a nice choice, as they are gentle and do very little to disturb the water. That's why so many breeders of fish use them in fry tanks.
There is also a thread on this site ( in the DIY section I believe ) showing how to make a small gentle filter using a fish food pot, gravel, filter wool, an airpump and airstone with tubing. Very simple. You could use that in a 2-3 gallon tank if commercial ones are still too strong.
There is no excuse not to have a filter. Really there isn't.