I'm ok with keeping a lid on magic items with the 3 attunements rule, though it does feel a bit odd from a roleplaying and fantasy perspective. "Sorry, Gandalf, you can be attuned to your staff, robe, and cloak, but not your scarf. Or your hat. That's too many. Laws of magic, or something, I guess."
Thr idea of tying the number of attunements to a stat is intriguing. What if it was tied to a character's lowest stat? Perhaps something like 3 + lowest stat modifier?