I don't think it is a BR problem. Multiplayer FPS games have been in a weird place for a couple of years now. It used to be a BF or COD game launching was massive. If both dropped in the same season it was insane.
I think it is a simple loop of games taking a lot more resources to make. Companies are afraid to innovate and risk missing the mark, which will cost them millions if not billions. So, we get cookie cutter stuff. Much like what is going on with TV/movies/streaming.
I would argue BF Firestorm could have been something. It wasn't free to play and didn't get any support from the developer either way. Most Youtubers I watched liked it if they could have supported it. It didn't fail because it was a BR or gameplay. It failed because everyone knew BF V was struggling and that EA/Dice was never going to put anything into it.
Halo Infinite is the perfect example. A solid game with major content issues. I mean, people liked the gameplay for the first time in years. People liked the shooting mechanics and the gameplay, but there was nothing else there. Companies aim for live service and can't even put anything out but small amounts of cosmetics.
For all COD MW2/WZ2's "problems" (most invented by the internet), it is a largely successful game, mostly because they throw tons of studios and money at it. (IW has this stubborness about making games where they think they know what is right, and that arrogance pushes people away for good reason). The 6v6 game would be fun if not for the horrible engagement based matchmaking.
COD gets played because there's little else out there. I find myself playing Bf 2042 more, but that's obviously not for everyone.
We're stuck in this cookie cutter, lack of innovation land of "meh" games.