Interesting discussions.
We have added record-while-playng into Microstudio in the past, and it works awesome. It even has a way to absolutely align the recorded sound with the playing music, thus removing the two digital delays (play buffer, record buffer) so you can do true synchronized multi track recording.
We are planning to add record into Hoster in 2012.
FYI: If you are supplying the music, and giving a copy to the singer, YOU are violating copyright law in the USA. Having said that, do what you want. I wouldn't be surprised if RIAA doesn't start policing this.
In Hoster, we will present a warning message (disable if you want) when you play a song from the hard drive that was not imported using the "Singers Disc" button; i.e. importing the Singer's song and playing it while recording. THAT... is legal because they already own the music, not you.
MTU is not playing Karaoke Kop, but we do feel someone should keep the law in front of this industry.
Illegal copying has driven out most of the Karaoke Producers, reducing the selection you now have to choose from. 