Probably a budgetary issue for the show, I believe only Moldaver and the Enclave guards are the only energy weapon wielding characters in the show. Though I'm certainly happy that the Colt 10MM is given it's due in the show.

Could just be an artistic preference from the producers as well. Ballistic weapons are grittier (at least imo) which meshes better with the show.

Just my take on it.

The West Coast Brotherhood was almost annihilated by the NCR, and the war was technically over despite their repeated harassment of NCR citizens. They lost people, weaponry, resources, land.

In the TV show we witness them being reinforced by the East Coast Brotherhood, but that doesn't mean they're miraculously back up to their former glory. Especially when people like Dane, Maximus, Thadeus, and Titus (who is, admittedly, from the East) are essentially all they have to work with for the next generation.

They did send the prydwen which shove stock with a lot of troops and fire power.