wow there are some pretty bad misconceptions here...
so what, it is only one betta. would you get a filter for a tank with only ONE oscar or ONE angelfish? of course. bettas need a filter just like any other fish. in the wild, they do not live in tiny, perfect 2.5 gallon holes in the ground. they live in huge rice patties and ponds. bettas do use oxygen in the water, but also the atmosphere.
actually, bettas do have a pretty high bioload since they thrive on diets high in protien.
water changes are NOT good enough. ammonia will accumulate rather quickly in such a small tank, and DAILY water changes are needed if no filter is kept. and how long will that be kept up? not very long at all in all practicality. a filter lengthens the time you can go without water changes to 25% per week. that is much less than 75% per day.
a betta in a tank with a filter will ALWAYS be healthier than on in a tank with no filter, and thats just a fact. plus, filters like the Azoo Palm filter, with 13 gph, consume next to nothing when it comes to electricity. personally, i find it rather sad that anyone would think having such a tiny filter to keep an animal healthy is a "waste of electricity."
perhaps you would like to give up air conditioning? its just for comfort, you can survive without it.