How can anybody possibly use a preposition as an auxiliary verb? How is it supposed to make any sense?

If you mean things like "I would of done that", I think they are just going by the sound of the words. And since "have" as an auxiliary doesn't have the literal meaning of "to have" in the sense of possession, one can argue that the auxiliary verb is just a syntactic structure with little semantic content. So, it becomes understandable for someone to substitute "of" (having no sensible meaning) to replace "have" (which really does not have much meaning either when used this way) simply because the two sound similar.

It still grates on my nerves, however! 😄