Nothing wrong with transwarp beaming, IMO. It's technology from the future. That they didn't forget it shows continuity, something Trekkies usually appreciate.
They even plausibly wrote it out of our heroes hands in this film - confiscated from Scotty by S31. Really, the only place said technology will be a "problem" is the novelverse. And I'm sure they'll think of something. At the very least...
(how can the signal travel faster than
a subspace signal - which can take hours or days to reach its destination
Only in the episodes and movies where said communication is not instant, which are wildly inconsistant and contradictory in Trek canon. In this film's version of Trek, Kirk phoned Scotty in San Francisco from the Enteprise at the Klingon border and Spock phoned his older self on New Vulcan from Earth orbit. No delays.
But even if Khan beamed himself off Earth and rematerialized on Kronos three days later, so what?