Historical Digression Dept. They're called mechanical royalties because back in the day when player pianos were the rage (and they were crazy popular up until radio fully arrived in the mid-1920s) the makers of piano rolls didn't pay songwriters because they argued you couldn't "see" the music on a piano roll like you could see it on sheet music. Songwriters got the law changed so that they got paid for 'mechanical' versions of songs (regardless of whether you could see the musical notes). The mechanical rate has always been a few pennies (back in the days of the Beatles, it was two cents) and in the whole history of the music business, artists and record companies never had to pay more than a dime per song per copy.
Right, you had a question. It's possible for the artist to pay the songwriter less than the government rate. That happens a lot with record deals where the record company pays less -- typically 3/4 of the compulsory rate (unofficially known as "the three-quarter rate"). But paying more for a compulsory license seems kind of kooky. And we should also mention that: (1) this rule is for cover songs--new versions of already published songs and (2) your cover shouldn't materially alter the composition. 95% of covers don't -- they keep the basic melody and chord structure even if they create a new arrangement -- and for the remaining five percent (think Devo's version of Satisfaction), they're probably okay anyway but keep in mind that a songwriter could arguably refuse if the cover materially altered the composition.That's because Section 115 of the Copyright Act provides that the cover arrangement "shall not change the basic melody or character of the work, and shall not be subject to protection as a derivative work...except with the express consent of the copyright owner." You can read more about the process here and here.