Are we proposing a system where a person can, perhaps even anonymously, get a song struck from the list without any discussion?
I would suggest a basic review of the submissions by some designated person (say, the karaoke master, since ultimately he/she is responsible for maintaining the list of available songs), if there’s any evidence of malicious abuse of the system. But as @Thalandor46 says, while it puts a lot of faith in the Sea Monkey community, it’s a very good community in which to place that kind of faith.
In the end, it comes down to song or people: which takes priority? I’ll go with the people.