I don't care, what lawsuits say. My Tiefling warlock has her powers from Cthulhu in my headcanon.
Tbh I know D&d groups that play Cthulhu crossover with homebrew rules.
I guess the problem here is, that you aren't really supposed to kill a GOO or an Elder God, so it might end very deadly for your characters. And as a rule (at least in our groups) you put much more time and effort into making a D&D- character than one for Call of Cthulhu, because you just know, that the latter one will eventually go mad and/or die.
The problem is that in Lovecraft's universe whoever got mixed in the web of the Ancients ones will at the end loss his sanity and if that doesn't happen the one involved will be emotionally crippled and scarred for all their life. Something in stark constrast with a set that revolves around adventurers able to succesfully complete a complex principal quest.