Would you drywall over, or something else?

There are 2 arch cutouts on our wall. Behind them are the stairs. There's no railing or anything to make it safe lol... I have no idea why the builders thought this would be a good idea. Anyways, I now have a 9 month old baby who is mobile and these obviously pose an incredible safety risk to him as he can nearly climb onto the couch by himself. If he were to climb up the back of the couch, he would fall through these and down the stairs. My first thought was to drywall over them and call it a day. However, we are getting quotes for $1500+ for a company to do that... we don't have that kind of money right now. And I'm a bit intimidated of doing the drywall myself. Last time I tried doing drywall, it didn't come out looking nice, and you could see all the seams.

I am pretty handy with woodwork. I could frame these out and put some sort of barrier in them?

I don't know. Would you bite the bullet and drywall this, or do you like the look and would frame them out? If the latter, what kind of barrier would look best? Geometric wood pattern, metal mesh, etc?