First, it would help to know what size tank and do you have any other filtration?
Airstones have a variety of uses, from purely aesthetic to very functional.
Functionally, they serve to reduce the size of bubbles produced and the smaller bubbles a) look better depending on your preference, B) don't make as much noise, C) move a lot more water around due to the smaller bubbles large surface/volume ratio, D) dissolve more O2 into the water due to the small bubble size, BUT the amount of O2 gained this way is much less than when E) The bubbles stir up the surface, break up surface scum, move water around and increase the air/water exchange of gasses like oxygen and carbon dioxide. So the short answer, is, yes they can be useful even in a betta tank.
I use airstones in a variety of ways in several, but not all, of my tanks. In my 100 gallon, I use airstones to drive my sponge filters and use a long air "wand" buried under some rock to give a bubble decorative effect. Do I need the long wand of air? No, but I like the way it looks!