The first part of my working life was spent in an accounting office which taught me that I hate counting, and for that reason I avoid counting mites. I am hopeful that incorporating a brood break and keeping bees in 5 over 5 frame nucs will allow me to avoid worrying about mites.
I think that between Mike Palmers (MP) nuc method, and Mel Disselkoen's "Outbreeding the mite theory" is the sweet spot in maintaining an apiary free of mite treatments.
Mike's nucleus methods are well documented here, but Mel's are less so. The OP asked if there was any scientific evidence to support the brood break as a viable method of mite control, and in a nutshell I haven't seen any.
MP observes that his nucs don't need treating for mites but doesn't posit any theories as to why, and in addition to the nucs he overwinters colonies in 2 deeps and a medium (if memory serves).
Mel starts a fresh queen laying after June 22 from a split, and overwinters in a single here in the midwest. Roland overwinters in a single. I am overwintering the majority of my colonies in 5 over 5 frame nucs.
5 of my 18 nucs did not get a brood break this summer, and I am curious to see their survival rate as compared to my others that by spring will have endured two brood breaks - the one where their queen emerged and waited then mated and the other enforced by winter.
I haven't treated my production colonies for mites. I have 11/12 alive so far in 10 frame equipment. Yesterday it was -16F in the morning, and all my mites are phoretic. If my production colonies live I intend to take a leaf out of MP's book (please hurry up and write one) and use the best as a basis for nuc making. I will consider surviving production colonies a bonus, otherwise I think of them as caretakers of comb for next years splits.
I will throw out another complimentary theory here that comes from processing the anecdotal evidence from the extensive experience of MP, Mel, and Roland. What if the answer is what the bees tell as when they want to swarm? They want a cavity the size of a single deep. They want this volume because it is the size that they have evolved to overwinter in most successfully, and, for undetermined reasons, this volume best suits the bee and the numbers therein least suit the mites.