I don't like the idea of spending money on a game that's online-only with no offline single-player elements. What happens in the future when people stop playing? Or when the next generation of systems is released and the servers go offline? Seems like the game would be kinda useless at that point.
I'm only speaking from the PC side...but all of Blizzards games are still playable. Servers are still live for Diablo 2 (hosted by Blizzard) and it came out almost 17 years ago. No need for next generation systems when all you have to do to your pc is update it every so often.
I personally feel that Overwatch will be around for a long time, or until it has a replacement for it that carries it into the next game. And then games like TF2 have been around since 07 and is strictly online. When it's PC, there is no limitations.
Let's also mention that Blizzard will keep doing events for OW, new skins, new characters, no play modes, battle arenas, maps...there's no end for them. One of the few companies I trust I'll get a quality game out of no matter what type of game it is.