Earlier quoted context omitted.
Since when do cover artists pay royalties?
There's a difference between covering a song in a recording and being a cover artist. With the latter I don't find a consistent answer. I've read venues pay a licensing fee, and that depending on prop use it could cost more, etc. If you cover a song in recording, re-arrange it, whatever, you pay royalties to the original songwriter.
IIRC, the licensing fee paid by the venue doesn't necessarily grant the performers any rights, it just waives the venue's liability. The nature of the relationship between the performer and venue is context dependent and it isn't always clear if the performers are covered or even could be covered by the venue's license, anyhow.
In practice the licensor associations will leave the performers alone as long as the venue has a license, because what's the point of the venue license if artists face legal jeopardy for playing there.
Alot of copyright works this way: the edges are very blurry and the incredibly broad scope of claims and defenses effectively corrals everybody into quasi-legal arrangements. Were it not for criminal liability and potential for ruinous monetary damages, this would definitely be a feature more than a bug. It's certainly deliberate. No law could ever be precise enough to properly balance such interests a priori.