The pitching coach can call the game instead of the catcher. That happens all the time.
The catcher will still be expected to receive pitches and help control the running game. The latter seems less relevant in this era because teams don't steal that many bases, but it is still the #1 criteria that weeds out catchers defensively and contributes to the lack of offense. Players have to achieve a minimum pop time, or they can't play catcher in MLB.
The strategy may change with sinkers at the bottom of the zone. ABS will get those pitches called a strike and you'll need a catcher who can block the ball in the dirt.
I think there will still be defensive specialist catchers, but the emphasis will shift from framing to blocking pitches and controlling the running game.
A drop in stolen bases is a foreseeable unintended consequence of ABS. If the catcher no longer needs to frame pitches, they can set up to receive pitches in a stance that allows them to decrease their pop time. Instead of framing the pitch in the middle of the zone for the umpire, they can receive it like a pitch out and ready themselves to throw a few tenths of a second faster.