Interesting paper -- thanks!

It seems to me to argue not that the Bohmian stance is that the wavefunction isn't a thing, but that one good Bohmian stance is that the wavefunction isn't a thing. Of course that might suffice as a rebuttal to the common claim that Bohmian mechanics is basically a less honest version of MWI plus some extra unnecessary bits.

... Though the paper's approach doesn't seem perfectly satisfactory to me -- the proposal is that the universal wavefunction should be considered a law of nature, which seems to me about as reasonable as considering every fact about the universe a "law of nature" and doing away with contingency altogether. I confess that I don't have much in the way of actual arguments against doing this, though. It just seems to violate a general pattern I think I see, that it works best to put random-contingent-looking stuff in (so to speak) the data rather than the code.

(... And: even if we deny that the wavefunction is a thing, the usual argument still seems to me to have considerable force: Bohmian mechanics includes all the same stuff as Everettian, even if it reclassifies some bits as laws rather than things, plus extra stuff -- all those ontologically basic particles -- that seems to serve no purpose beyond making the theory feel a bit more natural to some physicists.)

It might turn out (I suspect only with a complete theory of quantum gravity in hand) that actually there's a really briefly specifiable universal wavefunction that naturally gets everything we see as one of its branches. In that case, my objection to treating the wavefunction as a law of nature rather than a part of nature would probably go away. I'm not sure it would really do much to make Bohmian QM look better than Everettian, though.

(Disclaimer: I'm not really a physicist or a philosopher of science, and my intuitions on this stuff aren't worth very much.)