Jason, the right answer is always, "It depends." For some, double pressing will improve shoulder and t-spine mobility and for others it will be too much. It goes back to one of our core training concepts - find an appropriate challenge, not something that's difficult to do even once in good form, and go from there.
I like an empty stick or a rubber band and doing dislocates and overhead squats - I feel there's less room to hide a mobility problem there and, as you said about double presses, the OHS is a movement that, for me, seems to help improve my shoulder and t-spine mobility.
Thank you for offering a counterpoint - always welcomed and always appreciated.
-S-