I see beekeeping as being a "nickel and dime' approach to success. The right management strategy, the right genetics, and the right equipment, all go together in making differences between 10% loss and 60% loss.
Studies I have seen, suggest a mite decrease from 7 to 15%. Nothing unto itself being able to solve any mite problems. One study out of Cornell, because it fails within the statistical realm of being negligible, has said SBB as useless. But I'll take that 7% decrease in mites. I'll take every 5% advantage I can get.
I think for much of SBB impact on mite levels, it is directly in relation to what type bees you have. Not the labeling of bees. but how hygienic they are from a grooming standpoint. Bees obviously that are good groomers, will knock off more mites. Bees also stimulated with trigger mechanisms (smoke, oils, etc.) also will groom off more mites. To just slap on a SBB and not have good grooming bees is not going to cut it. And not all bees are equal when it comes to grooming.
People always ask me about leaving the screen open or closed. I keep all mine open year-round. Of course, I am also big on the importance of selecting a good apiary location where wind is not an issue. And when retained heat means the most, that being late winter/early spring, most clusters are up in the second box, far from the SBB. So this issue of lost brood is always questionable to me. It may be an issue when some swap boxes in the spring. But that's just something to guard against and know with SBB, you can not do it too early.
I think SBB are worth it for many reasons, including mite drop (using good grooming bees), increased air flow, etc.