So I guess a tune o matic would just slot straight in?
First of all - the bridge on a JM, Jag and Mustang rock back and forth with the whammy. So you dive bomb and the strings slide a bit over the bridge nd then when you return the bridge gets pulled back out and flat. And vice versa.
Gibson have thinner necks and a different string spread, however there are versions of Tune-omatics that fit like the one on the J Mascis JM (great guitar). Different post spacing on a Gibson too.
I use a roller bridge. No rocking, no drifting out of tune with the whammy. There aren't many alternatives that fit. Guitarfetish have a cheap one for a Tele. I throw away the plate and stick little bolts wrapped/taped, with a nut on into the bridge thimble. A bit fiddle but they work a treat and very easy to adjust intonation. Correct Fender string spread. I use on my JM, Mustang and Jag. No more tuning issues! Depending on the neck heel thickness they might need a shim. The Mustang did. Don't believe the crap about roller bridges and sustain or tone. Total bollocks.