It’s a “Who will bell the cat” kind of question. The mice know the cat is there, and that belling it will warn them. But getting the bell on the cat without getting eaten is a whole nother matter.
Reminds me of something I saw on a wildlife show the other day... This huge herd of wildebeests was trying to cross a river that they knew concealed a bunch of 15 foot crocodiles. (Just the head on one of those things looked as big as a sedan.) Finally, a couple of them jumped into the water *CHOMP* Then once the rest of the herd could see where all the crocs were, they ran the other way and crossed further downstream. Definitely wouldn’t want to be the trailblazer in that situation.