Hopefully during the course of this film series, alternate Kirk will have an Excelsior class starship because I believe that Prime Kirk wasn't really due for retirement in the Prime Reality. He only needs a new ship and the new ship(s) available is the Excelsior class.
Also in this new film series, kindly remove the animosity/nostalgic behavior of Scotty towards new ship/Constitution class. It's not helping Kirk and his crew with their careers.
I know. Since the size of the alternate reality Constitution class starship has been blown up to over 600 meters (I've heard everything from 600m to 900m), I calculated that if the exact proportionality between the AR Connie and the AR Excelsior were maintained, and if we take the 760m length for the AR Connie from "Experience the Enterprise," then the AR Excelsior would have to be 1,140 meters long - the size of a Venator-class Star Destroyer from "Star Wars: The Clone Wars!"
I think the idea is that, within the Trek canon, a Transwarp drive would be a bit like the Hyperdrive from Star Wars, and allow one to traverse the entire galaxy in a matter of days, rather than decades.
Hopefully, Star Trek will not feature the Fed and other Alpha/Beta Quadrant civs making quite such a discovery for the time being.