>>18466535boots are actually less formal, since they're for outdoor use. notice the broguing in your example.
you're implying that it is the height of the footwear that makes it more formal. this silly, since when dress boots were a thing they were a slightly dressier alternative to the giant hessian boots worn by horsemen.
also the most formal style of shoe of all is the court pump, which is cut even lower than a loafer.