Why is so much music recorded out of key?

It's more important that the musicians are in tune with each than with concert tuning.  Analog recording and manufacturing had numerous places where small errors in pitch could occur.  The biggest selling jazz album of all time, "Kind Of Blue", had pitch/speed issues.  I can imagine for someone with perfect pitch that it could be annoying, but for most it doesn't matter.  With digital recordings you can intentionally pitch up or down to your heart's content.  It's just another FX tool.

Check out pages 55,56 of the book God, No! for a rational take on the subject.

Hmm: having @fuzztone answer this particular question has a certain Je ne sais quoi….

Doesn't bother me and I doubt I'd be able to tell; these are not quizzes or tests, just music that one either enjoys or does not. 

Lots of things may happen when music is committed to recording, not least of which is that the players were not tuned to a perfect 440 or whatever to begin with.
There’s no such thing as being “off key,” only “off pitch” which refers to an instrument or vocal not being in pitch with whatever frequency the music is tuned to. There’s no law that says we have to be at 440. One may prefer something different (likely a little lower…there’s a whole thing with 432 Hz)