In my my mind, the Watcher in Logopolis is like K'Enpo in Planet of Spiders: His future self. However, unlike that situation, the Doctor's Watcher is just like the Doctor himself: Chaos personified. K'Enpo, being the future self of the Hermit, is just his present self, a literal prototype of composure, knowledge and wisdom. He knows and understands how regeneration works, in a way the Doctor never has or ever wants to. He's in harmony with his future projection and allows it to take his place, making for a seamless transition. Whereas the Doctor is rarely ever in good company when he meets even his past incarnations by mistake or otherwise. He's in complete disharmony with his future, and none more so than the Fourth Doctor, who might've gone on forever where it not for Almost Five knocking on his door.
In short, the Watcher is Five, who should've arrived by now, IMO. Its the Time Lords version of the Grim Reaper - only, he's not Death, he's the Regeneration.
Hence why Four regenerates from a fall his future selves could walk away from - the fall didn't fatally wound him. Didn't even hurt him that much. Having defeated the Master after getting his eviction notice from the Watcher, he was simply ready to go, and knew the fall would be a pretext his companions wouldn't even question.