In the US, artists don't get to 'allow' for covers or not. The words and composition of a song are covered under a mechanical license. The recording and perform

In the US, artists don't get to 'allow' for covers or not. The words and composition of a song are covered under a mechanical license. The recording and performance is covered under a different license. Under U.S. law, the mechanical license is a compulsory license - the rightsholder must give a license to anyone who applies and pays for it. The payment is standardized and includes royalties, so it's a pretty good deal for anyone who writes a song that gets a popular cover.