Here's a thought. If the song you want to cover has already been covered a hundred times, and the most popular covers have commercials on the front end, that probably means that the publisher would rather leave the covers up make a little money off them ("monetize") than be sending injunctions all the time. If you want to cover a really popular song and you don't see many covers on YouTube, that might mean that particular publisher hasn't "got with the program" yet.
I was thinking about covering a song that is by a very popular band. One of their songs has about 1000 covers, and the most popular ones are "monetized," so I should be safe, right?
But the song I wanted to cover only has one cover, and it's so bad that YouTube's melody detection software hasn't figured it out yet. It's from a different album than the other song, so maybe it's a different publisher. Time to read the liner notes.