That's a matter of preference of course, but I think Stevie would disagree with you, since that's also how he plays it live. He plays the top part, and has another keyboardist play the bottom part. If you see live videos of him playing it back in the day, before he had a second keyboardist in the band, he had the guitarist cop the bottom part (as close as he could anyway). That's how I handle it in a band with a guitarist; make him learn that part. They can't get the low E-flat of course (unless they tune down), but the line in thirds is easy enough, and basic mute string scratching covers the right-hand chords.
When I play it without a guitarist, I've developed a part that's as close as I can get to playing both parts simultaneously. It's not every note, obviously, but it captures the most essential elements of of both parts. Then I also have an even more simplified version of that part that I play with only the left hand, while playing the horn line with the right. That actually turns it into a fun and challenging tune to play instead of just another lame cover.
The other thing I'm picky about are the chords in the chorus, which hardly anyone ever plays right:
Bb7 B7(b5) Bb7 A7(b5) Ab9sus Bb7(#5)
Do you have a transcription available for your simplified part without horns? I couldn't imagine playing this part and covering horn parts as well. Of course, I can't figure out cover bands without keyboardists that even attempt this tune.