Actually you can do that! If you transplanted a stock strat middle pickup into a Les Paul or other "Gibson like guitar, and played it using the single coil middle pickup, it would sound "more" strat like then the humbucking bridge or neck pickup. You would also be able to tune the guitar, something a strat can never quite can do.You can't put single coils in a gibson and get it to sound like a fender or double coils in a fender and make it sound like a gibson...the thing sounded pretty much like a fender.
If you bent one string, the rest would stay in tune, unlike a strat.
Likewise if you transplanted a gibson like humbucker into the neck position of a strat, it would sound more gibson like than the stock fender single coil. Of course, even after transplanting the humbucker into the strat, the strat would still not be in tune, and certainly would not be in tune after you worked the wammy bar.
Certainly the scale length differences would not go away.
Jerry liked the single coil pickups, and the scale length. He did not apparently like strats, again he de-strat-i- fied Alligator to the point of Alligator not really being all that strat like. Of Course Jerry liked to play a guitar that could be played in tune (who doesn't?).