Says the guy whose never had broad mite.
Sulphur may kill some insects it touches but that's it. Its not going to kill an insect that lands on the plant after the fact. It may harm insects that are there to rec the full brunt of the spray but that all. Sulphur is a far stretch systemic insecticides which are the real nasties for beneficial insects..
I would think that most people would want to get their plants on the mend quicker than what parasitic mites could muster. That takes time..they need to breed, multiply and establish themselves.
I agree it would be a good idea a couple weeks after you have sprayed to help keep them away & get some beneficials on the job to keep things in check, but I cant see it being the most effective way forward for dealing with an already established and serious infestation.
I may be wrong about the overall effectiveness of the beneficial mites vs broad mite, iv never used them. (and I don't think you have either) But I speak from direct experience in regards to the sulphur and it works.
Sulphur has been the cure for these kinds of things for...ever.
Real men use sulphur
Hipsters use beneficial mites