If a major website starting blocking user agents for any reason other than compatibility then all that would do is trigger (finally) the deprecation of user agents strings as browsers would all just pretend to be each other.
It would just be yet another zero-sum meta-war, with web browsers ultimately using randomized user agent strings just as mobiles randomize MAC addresses.
But none of that means that the war somehow can't or won't occur.
If a major website starting blocking user agents for any reason other than compatibility then all that would do is trigger (finally) the deprecation of user agents strings as browsers would all just pretend to be each other.