Because that's the way ASCAP et al. bribed Congress to write the rules. They're not stupid. They understand that if they charged bands to cover other people's tunes, bands wouldn't be able to afford to do so and thus would either write their own music or go out of business. So they write laws to exempt the musicians from paying for music while making the venue owners (the deeper pockets) pay.
What's more, in the days of vaudeville, songwriters got their money selling sheet music (50 cents a booklet, big money back 100 years ago). They encouraged performers to sing their songs; they would bribe a shill to sing along from the audience or down the street at the local pub all to convince the audience, potential customers, that the song was "popular" and that other people were already singing it.
When recorded songs first came along, there was no money paid to the songwriter (certainly no royalty payment). When radio came along, there was no royalty payment for playing records. Heck, record companies gave the radio stations plenty of free records to encourage them to play their songs. Live musicians complained that they were being forced out of work.
At every step of the game, the Supreme Court said that this was all fair use. Every time, the industry came back to fight to change copyright law.
This continues to today. We have the "best" government money can buy. The founding fathers would not be happy.