I never play with midi files either for the same reason, prefering to convert them to styles that mirror each individual song arrangement so I can play left hand and control everything.
But mp3s are in a completely different ball park altogether. In exchange for giving up left hand control you get the real orchestral backing, for instance you play along with the true Nelson Riddle arrangement with real strings and real brass stabs. It is surprising how good the soloist voices are in combination with a real orchestral backing. So if you never try it you won't know what your missing. There is no keyboard on earth now or in the foreseeable future that can produce a sound like this. Not for every song maybe, but a very interesting and promising alternative.
No secret, Bud, try the free downloads at
http://www.singingstation.com/