I feel like removing umps in favour of the computer would be a bit too drastic. An easier solution would be to install a system like what they have in Tennis where you get a certain number of challenges. If a team challenges that specific strike you look at the Jumbotron where a pitch tracker comes up and says whether or not it is a strike or not. It would only take 10-15 seconds not like the replays that they do now.
I think a system like this would help the umpires more than anything because they would have to call the strikezone by the book and they can't say "I call the outside strike" even though its not an actual strike.