Personally, I actually think retrocausality, once you twist your brain around it, is another perfectly sensible option that doesn't involve multiplying the universe into a near-infinity of inaccessible, unobservable parallels. The solution in my mind is that retrocausality actually isn't; what it means instead is that what "the present" is is even less like what you thought it was, and is even more of a partial order than relativity already told us it was. The answer to the "double-slit" experiment, to my mind, is that there simply isn't a "before" and "after" and some sort of "retrocausal self-interference" of the wave... the whole thing is simply one atomic event that doesn't have a before and an after, and your imposition of a temporal order on the events is much simplified from the reality. The mystery lies in your attempt to impose a global temporal order, which is appropriate enough at scale, onto a single local event where it doesn't apply in the way you expect. The results of the double-slit experiment itself is not that mysterious, merely counterintuitive, once you release the small scale from your imposed large-scale idea of how time flows.
It means that "the present" is actually quite complicated in a quantum universe with as many qubits as ours has, but, just as QM may be counterintuitive but eventually looks classical at a large enough scale, time may in fact be massively complicated but at scale it still works as we expect.
It would have a "physical basis" to it if you could visit the alternatives somehow, in which case they could be demonstrated to physically exist and all doubt would be removed. But so far that is not on offer.
"Entia non sunt multiplicanda praeter necessitatem" and all that.
The entire wave-function is there in the theory, containing all the "worlds" and it's responsible for 100% of the dynamics.
Additionally, Bohmians add a single "world particle" indicating which world we are in, and it's guided by the wavefunction. They claim only that particle is "real", but since it has no effect on the state of the universe, I would call it the only part of the theory which isn't real.
It's not about a simple explanation, it's about explaining using simple things.
A wave is simpler than "infinite worlds"
The "worlds" are just approximate ways of slicing up the wavefunction which correspond to our sense of classical reality. They are clearly (and uncontroversially) identifiable if you run a simulation.