[loup-vaillant]

Many Worlds is popular for a reason: it's one of the simplest interpretation that fits the facts. The scientist in you might dislike that it came about later than the Copenhagen interpretation without any experiment to distinguish them. The Bayesian in me just applies Occam's razor.

Just realize that a collapse interpretation is the same as a many worlds, with the additional assumption that the blob of amplitude you don't live in is somehow flattened to zero. The "it's just maths" interpretation isn't much better: the maths tell us that we have two worlds worth of amplitudes, yet for some reason the one we don't observe isn't real. This is as ridiculous as believing that stuff you send outside the observable universe ceases to exist once it crosses the boundary.

As for how far it pushes non-determinism… I'd say quite far. Under the MWI, the universe is entirely deterministic. What is not is just our subjective experience. What was originally a Physics problem is now an *anthropic" problem, similar to what you would get if you were to copy & paste humans, or do mind uploading. The more interesting mystery in my opinion is more about why the Born statistics are the way they are, instead whatever else we could imagine them to be.