That and because thematically, it's harder to use an already well established core body of mystical mumbo-jumbo. The ONLY people that would have been interested in that, would have been people who have already studied those things. From a perspective of "I just want to tell a fucking story goddamit!", being able to shape that clay any way you want has definite advantages. That would be the real reason Rowling avoided the things I mentioned, if you ask me.
She wanted to create a setting that could be both light-hearted and fun, sufficiently similar to the daily grind of modern children so that the characters were relatable, and still be able to mature into a dark and dramatic work of fiction later. You don't get that with dusty and well-trodden magical traditions.
(EG, waxing philosophically about the numerological meaning behind Lord Voldermort's chosen name, and on the
seferical construct, and how it relates to the creation of a horcrux, would not be interesting to anyone except somebody who is just really fucking into studying realworld mysticism. It would get in the way of "Voldermort hated his own heritage, could not experience or feel love, and the exact mechanics of the spell he used to make the horcrux is only important in that he had to murder somebody to make it work." Doing the latter pretty much requires one to abandon actual examples of magic from our real world, and invent a new magic from whole cloth, and only convey narratively meaningful information.)