bluethief: I don't think it'll happen. It's a different situation compared to the Bethesda launcher, IMO.

Battle.net has always been the exclusive launcher for Blizzard games, and more recently Activision games.

Bethesda launcher on the other hand, doesn't have exclusives. All games release on Steam at the same time. And it isn't even required to run if you play a game through Steam, like Uplay and Origin do.
Also, the news that it'll die shouldn't actually be a shock. Since they announced that Deathloop would be changing to Steam keys on third party sites, the writing was on the wall that something was going to happen.

We don't know what the future will be once they're under Microsoft wing, but I guess Activision/Blizzard will be it's own vertical inside Xbox, so it will still preserve some kind of independence, and I don't see them getting rid of Battle.net.

However, there's one way it can also be retired like the Bethesda one. Microsoft will be wanting to put all of their titles on GamePass PC, and that runs on the Xbox/Windows App. So will Call of Duty have a Windows Store build + a Battle.net one? Will it still require Battle.net running alongside the Windows Store? Will the games even start come to Steam like other Microsoft owned ones? Whatever the case, it'll be interesting to see what happens.