Hair algae can sometimes be caused by old light bulbs, wrong color temp light, light on too long or not longer enough, lights too close to the water, dirty partition between light and water.
Very few fish or inverts will eat hair algae and you don't want to add other livestock for algae problems anyway. You add more livestock because you want them and can house and care for them properly.
Cleanup and algae removal is our job.....
It is normal and expected to have some species of algae in a container of water that has light and nutrients, some species can be a sign of a healthy system, help make the tank look more natural by softening edges and provides area and food for microorganisms that the Betta can graze on for added nutrition. Not all algae is bad, however, since this is a closed system it is our job to keep it controlled and manually remove it on a regular basis along with our regular water changes.
You can limit/control some of the algae to a degree.
I use an old tooth brush and twirl it around my hair algae to remove on a regular basis.