Change your preferences so you create a take folder when cycle recording. When done recording, click the comp and select "Unpack to New Tracks". Done. The "Create Tracks and Mute" option does only create tracks assigned to the same channel strip, making it impossible to play all tracks simultaneously...
This appears to be as close to a solution as we're going to get: thank you JakobP!
It still involves creating multiple tracks -- as opposed to just one track, with all the takes combined -- but at least you don't have to create the multiple tracks beforehand, and do the whole process in several separate takes, which is something.
I do wonder why Logic Pro doesn't have a feature like the one Bobby Huff used in the video I posted: it looks to me like he just recorded in a loop and then had a track full of the combined takes when he stopped recording, which seems like a good feature to have.
Anyway, thanks again to everyone here who helped out with this question.