Once a proper meta forms in Overwatch and teams work out what they're doing (both in terms of strats and dm) then I think the game might become interesting to watch if they put a good spectator mode in. However I really do feel they run the risk of teamplays seeming somewhat underwhelming because of the lack of high mechanical skill ceiling (In terms of fps dm or moba mechanics).
The game reminds me of another game I've played a lot of, Awesomenauts. That's a fast paced game that's effectively a cross between a platformer/fighting game like smash and a moba. It has a small comp scene but I've never found it particularly interesting to watch, as although people come up with some clever strats and teamcomps which win them games, I've never found good plays particularly interesting to watch in that game, because the mechanical skill just isn't as high as a game like smash, and there's less to think about than in a game like dota. There's definitely a lot of skill based mechanics in the game, but it's not quite coherent, and comebacks don't tend to happen.
Still, I think it's to be expected that comp matches look like a massive clusterfuck when the game is still in beta, look at any 6es from 2007-08 and you'd probably think it was shitty as well.