Hey, I use lots of discarded sheep wool in my compost heaps
(clippings from the shearing shed floor)

We do the same (on a smaller scale) with cat and dog hair (which gets
recovered from any imaginable corner of the house).

...no weird weeds have resulted, which is rather disappointing. What am
I doing wrong? :-)

You need to be shearing alien sheep from outer space. That's where
the truly weird human-eating weeds come from in old movies, right?