Fat and connecting tissue melts with heat, that's what gelatin is.

Time and heat=fallapart dry meat. Balance heat and time to have it fall apart and not be dry, but you can't perfectly have both. Sous vide, lowest possible foodsafe temp and long time works pretty good, but you still don't want to go overboard.

Also, everybody likes the mallard reaction and browning and you don't get that with low heat (like 129F).

If all you want is fall-apart meat, that's easy, though, just render all the connective tissues into liquid.