How dare they take money away from Star Trek!!!!!
Functionally speaking, they haven't. The thing is, what with the taxes in LA and the bloated and inefficient filmmaking industry in Hollywood, a lot of the budget of the past two movies didn't actually go into the movies themselves. Moving production out of LA lets them put the same amount of money on the screen while saving money overall.
Really, though, I think cutting the budget would be a good thing. With a tighter budget, the next film might have to focus less on spectacle and effects and more on character and story. I think the Abrams films have done pretty well overall with the characters, but the last one had some action scenes that went too far overboard and didn't really feel necessary. I wouldn't mind seeing that stuff dialed back some.