First of all, full disclosure, there is no scientific study that backs up the idea that small cell works except on Africanized bees. We have discussed it many times and I find the studies fatally flawed, but that is not the majority view.
Here's my view.
For a number of reasons, using small cell foundation helps. It is not a cure, it is not a treatment, it does not work by itself, nor does anyone who has been using it successfully for years say so. Dee Lusby pretty much originated the idea back in the days of trachael mites for whom it was originally intended. Varroa came later.
In my view, it works because mites do better in drone cells, having more space, longer time, and a greater food supply. Small cell likely in my view puts bees toward the bottom of the natural cell size range, further delineating somewhat the phenotypical differences between workers and drones. Therefore, the infestation is pushed more in the direction of the drones, leaving more of the workers unassailed by maladies and diseases carried and caused by the varroa mite. Additionally, the worker emergence time is shorter than that of the drone, limiting the amount of time that a female mite has to reproduce, and smaller workers appear to emerge even earlier than that, further giving the bees the advantage.
I will repeat that one must not rely only upon small cell as a panacea or a treatment or a cure. It is not. There are many other aspects to a successful treatment-free beekeeping program and has been shown, small cell is not always necessary. The main key is letting lines of bees unable to cope with diseases die out or replace them before they can. The process takes about three years in my experience. Personally, I also have ceased all forms of non-treatment manipulation and specialized equipment as I do not believe they should be necessary for the bees to survive and their continued use only serves to further elongate the process of winnowing the weak. Bees should be reliant upon absolutely nothing to keep them alive in my view. Given any decent box, they should be able to carry on by themselves for a decade or more without dying out.
Another aspect is having clean comb. This is especially important in the case of antibiotics as the use of antibiotics may be effective in eliminating bacterial infections, but leaves the hive inviting to infection upon the cessation of treatment.
Ultimately I believe (and the evidence of other successful long term treatment-free beekeepers bolsters my opinion) that the weak bees have to die to get bees that survive on their own. So that means you either need to let your bees die, or buy from someone like me who has already done the work for you. But that work will cost you money. You usually get what you pay for and buying cheap often means you buy twice so take that into account in budgeting.