SoundHound already did this long ago. It works pretty well.
So, I bought SoundHound 8+ years ago in a Google Market promotion offering several apps for pennies (10c, I guess?). Tried it without much hope and damn it, it worked well. Sometimes it goofed, but truth be told, it may be my problem.
Also, it had the ability to identify covers in a crowded bar, or non-playback live versions. Shazam, which was very popular at the time, admittedly couldn't do any of that - in their FAQ (which I could not find right now) they even told that if Shazam recognize a live version, it must be either a playback or a player with microsecond precision repeatability.