I'm sure I read a while back that whoever is making all these DC shows doesn't have the rights to put Batman on the small screen, which is why they've had to get creative with stuff like Gotham, Pennyworth, etc.
There's a TV show being released as a companion piece to the next batman movie, but I'm not sure that will even feature Batman himself.
They do have the rights, CW is owned by WB who also own DC.
They have always been a bit more protective of Batman for some reason or another, Smallville and Arrow both started out as TV Batman projects but they said "pick something else" each time, Smallville because Batman Begins (
though I think it was a Tim Burton remake still at that stage Edit: Was a Schumacher Batman: Year One remake) was in the works and they didn't want audience confusion with 2 Batmen. By the time Arrow came round they really didn't want to mess with the Nolanverse, but it's a bit more noticable as they do quite a bit of lifting with Batman's themes and badguys, at least in season 1.
I think if you pitched a good show these days though you could probably get it, whereas in years gone by it'd be a hard no, I'd spilt the difference and go live action Batman Beyond, though budget wise that wouldn't work on the CW.