Yeah, this makes sense. Into Darkness performed below expectations and reducing the budget is just good business sense. They did the same with Wrath of Khan and we all know how that turned out. If anything, a budget cut is a good thing. A smaller budget means less pressure for the film to succeed and more creative freedom for the writer and director.
Yes, I agree with what you're saying, but the budget cut for the next Bad Robot outing will likely be fairly trivial in comparison to the dramatic drop between TMP and TWOK.
From what I've read, you can count on pretty much the same production values and "on screen" money for Trek 3.