You actually do need a mechanical license to do covers ...
As a broad statement, this is wrong. A mechanical license is needed to distribute a cover (recording) in tangible form (physical or download). It is not required for performance, dramatic or synchronization.
This is one reason I rarely do covers anymore.
Why not? Nothing prevents you from performing them live. It is the owner of the club, venue or concert promoter who is liable to see that the rights holders are taken care of, not you.
Copyright law doesn't allow you to use someone else's music and give it away.
Although that’s the idea behind Copyright, Title 17 actually spells out a number of exceptions that allow one to use someone else’s music and give it away.
YouTube has a policy that monitizes a cover and remits the revenue to the copyright holder. If the copyright holder does not allow covers, i believe YouTube will remove the music. I'm not 100% up to speed on the YouTube monitization policy but I think that's fairly accurate.
Again, by making a broad statement, you are mistaken. Apparently, you don’t understand the term “cover” as it applies to the music business.
A cover is a copy of a
recording of song made by someone who is not the rights holder. Once a song has been published in the USA, the rights holder has no say about covers or broadcast. As long as the statutory license(es) are paid (or a lower figure negotiated directly with the publisher) for distribution, anyone can cover any previously published work. Although the Harry Fox Agency is a convenient way to obtain Mechanical Licenses, it is not required that you go through them—the Copyright law spells out a much less expensive way of obtaining these.
YouTube is not about covers, it’s about synchronization. This is putting a song to an image, still or moving, and making it available for public viewing. Without written permission from the publishers, they can deny this. Failure to obtain a sync license from the publisher can lead to takedown notices, suits for damages and all sorts of unpleasantries.