The factor to consider is the drone cycle. From egg to emergence of a drone is 24-25 days. Most mites are in drone brood.
Suppose you do a simple split. One half has a queen and all goes on as usual. No mite break.
The queenless half however has several different paths. If it must make a queen from an egg, then it will be about 1 month before the mites have new larvae to infect. The queen cycle is 16 days from egg to emerging from the cell, then a period of maturation, virgin flights and mating, then a while before egg laying starts. 30-40 days at best.
Sounds good, but a drone egg laid the same day of the split will emerge on day 24, eight days AFTER the queen emerged, and just a few days before she starts to lay. Most mites will be on young bees who are not flying, so attrition is low. Unless these bees are very serious about grooming and mite biting, the population of new, young mites is hardly reduced before they have new cells to invade. The older, adult mites are being lost during this period, but every day a new population of young mites is hatching along with the drones that are continuously hatching.
I would call this a 'pause' in mite reproduction, not a highly useful break. The queenright half got no break at all, and those mites are exploding and drift will carry them into the nearby hives.
It is even worse if the bees had a capped queen cell ready when you split, or if they swarmed. The hive left behind by a swarm will have capped queen cells ready to hatch, and the brood break is so short that drones are continuously hatching while the virgin is mating, returns and starts laying. Barely even a mite pause in reproduction.
Based on this I now believe my former thinking on brood breaks was naive and ill-informed. The mites are well-adapted to the bee life cycle and are prepared for normal events like swarms and queen replacements. Brood breaks of normal length will slow the mite cycle a bit, but not stop it. It's a 'better-than-nothing' intervention.
What are my next steps for TF? This year, after finding a badly infested drone comb, I started seriously working to eliminate drone brood after the swarm season. Pluse a second brood break in late July.