If every collapsing wave-function (i.e. every non-deterministic event) produces forkings in the Time Line, far more copies of 2020 exist than 1920s. This hardly matters before Time Travel is invented, but then it's shattering. Imagine setting your chronoscaph's controls for a spot from which to shoot Hitler. As you hit "Launch", some particle somewhere decays (or not). Now there are two of you heading for the same grassy knoll. Or more likely, zillions of you – not to mention time-tourists, assassins after his chauffeur, etc.… all appearing at that same point in space-time. KAPOW! Was that the Berlin in our past you just nuked?! Limiting Time Machines to interbranch rather than intrabranch Time Travel doesn't stop double hops (USA 2020 to Byzantium 1970 to Berlin 1920), and even if you can only travel through "probabilities", not time (USA 2020 to Byzantium 2020), your doppelgängers will follow you.
In the strict quantum-physical version, there is a solution: the unpredictable (non)appearance of a Time Machine is itself a world-forking event, so there is a Time Line (ours) where it didn't happen; one where only you appear; and others for every mathematical combination of arriving Time Travellers, including all the quantum-miracle Time Machines from nowhere. This makes the universe even more alarmingly uncontrollable; furthermore, it means you can't kill the original Hitler, or return to your home Time Line by Time Machine.
The Type Four Time Line cannot contain genuine Closed Loops or Loose Ends (though it can seem to), but it can still induce bafflement. The main problem with a cosmos where everything that's even remotely possible happens somewhere is that it undercuts the concept of probability, and of "causing" or "preventing" anything (thus destroying any narrative tension).