The thing that's weird is, I don't think this is normal at all. On Nintendo's end, you can still play Splatoon 2 just fine even though Splatoon 3 came out, even on multiplayer. Multiplayer games often have a long life after they're superceded, even if it's a smaller contingent. If you boot up Quake 3 Arena or Unreal Tournament 2004, you can see there are still players online pretty much always, even if it's a small contingent.
The only good reason I can think of for utterly axing old games is so that you don't have to compete with them. Why buy Reforged for $40 when you could get the original better Warcraft III on GoG? (You can't, of course; you can only get Warcraft I and II on GoG, at least now.) In case of Overwatch, they WOULD have to continue to run the servers. But surely, the majority of players would switch to the new game anyway, right?
My opinion should be taken as a grain of salt because Warcraft III is one of the last games I really liked that much from Blizzard, to be honest. But still, something stinks over at Activision Blizzard, and it's somehow not just Bobby Kotick.