I think the whole Warp speed thing is not so terrible.
It's more like Star Wars now, which isn't a bad thing. On Star Wars they also could jump around the galaxy rather quickly. And the SW galaxy still felt big and mysterious.
One problem is certainly that a five year mission isn't really a journey into the unexpected anymore when they can just warp (or beam) back to Earth every evening to rearm and have a few drinks.
Transwarp beaming is different though. It's hard to imagine a series without nerfing this.
If you think about it, though, the new "SW'ish Warp" reduces the "universe-shattering" effect of transwarp beaming. Because if you can have an armed ship anywhere in minutes you may prefer that over beaming people instead (and long-range beaming might have other complications and dangers they could always introduce later).
Loved the movie, disliked 09, STID's my fav ST movie now. Brainless and brutally fast-paced at times, but the heck. Cumberbatch and new Klings are badass.