But if the rights issue wasn't there, wouldn't Google build a competitor in a few days? It's a fairly simple website to make, and lyrics websites do a ton of traffic.

Google built something similar years ago--not a direct competitor to RapGenius, but rather a generic annotation platform for the Web.

Guess what? It's now discontinued: http://www.google.com/sidewiki/ It's not trivial to build annotation platforms that are both compelling and easy to use. Hat tip to RapGenius!

It is trivial to build a lyrics site, and it would be very helpful to search users who so often search for lyrics and wind up on shitty websites.

There was Apture which was doing similar. They got bought by Google last year.

http://techcrunch.com/2011/11/10/google-buys-contextual-rich...