The bodywork is 8/10th the time and cost. If you pay a pro for that, you might as well have them paint it.
A screwup with the paint can turn back into more sanding and body work. Would be a shame to see it perfect in primer, then have to redo it again and wind up 50% over budget..
You're not missing much by letting someone else do the paint. You can always shoot smaller panels and engines and transmissions with all manner of colors, and much lower stakes if there's a run or wrinkle.