Analog tape under the best circumstance is equivalent to 13 bit digital.
Not really. Analog tape can reach 20kHz and beyond - you can't do that with 13 bit digital. That makes your comparison meaningless.
What most people decribe as an improved sound is just a gain difference.
Or distortion.
I had a Revox A77 for a decade. None of my tapes sounded better than the record.
Agreed - there's no way that a tape dub can be more accurate than the source. Tape was great for making custom mixes when there was no alternative, but I don't see the sense in doing that today.