I also agree there is no consensus that the problem of getting Born's rule from the Schrodinger equation has been solved to everyone's satisfaction.
Andrew Gelman calls it a "tabloid": https://statmodeling.stat.columbia.edu/2014/06/17/hurricanes....
I will check the paper out though.
[0] https://www.science.org/content/blog-post/no-more-prearrange...
Edit: I read the paper. It is borderline crank work. There are decent arguments for the Born rule in MWI but this is not one of them. (I like David Wallace's book, for example.)
One basic problem is that using symmetry arguments to justify the assignment of subjective probabilities (cf. page 4, right column) is going to fail when there isn't a symmetry available, for example for irrational probabilities.
A deeper issue is the implicit assumption that one can coarse-grain into discrete "effectively distinguishable universes" for the purpose of doing these counting arguments. There are significant conceptual difficulties doing this, and this claim is much stronger than the bare MWI. Wallace discusses this at length; see for instance the citations in the blog post you responded to.