I've heard about this same issue/request many times over the years with regard to the PSR-E models. Since it was brought up by different people, they all weren't necessarily wanting to do the same thing, but the general request is to be able to select part of a MIDI song file and loop it while the keyboardist-- and possibly other band members-- play solos and jam along to the loop.
Eileen said that this can be done on the Tyros and Genos models. I would have thought that it could also be done on the PSR-S models without the insertion of the extra count-off measure at the beginning of each iteration of the loop, since the PSR-S models don't have the Yamaha Education Suite (or Y.E.S.), and I thought that the A-B Repeat with the count-off measure was a function of the Y.E.S. feature.
Anyway, a Style might appear to be an ideal alternative, but the keyboardist still wants to play the MIDI song normally both before and after the looped portion-- so if a Style were to be used, it would probably require a lengthy Intro that plays all of the song that comes before where the loop is to begin, as well as a lengthy Ending that plays all of the song that comes after the loop, which is doable. However, a Style has only 8 parts (or channels), whereas a Song has up to 16 parts, so aside from the problem of having to take a MIDI song file and convert it into a Style with a very long Intro, a Main loop, and a very long Ending, there's also the problem of trying to squeeze up to 16 channels of a "backing track" into no more than 8 Style parts, which might not be feasible. Plus, the band might change their minds about which portion of the song they want to loop-- for instance, do they want to take turns playing solos between the second and third verses, or after the fourth instance of the chorus, or do they want to skip the solos entirely and just play the "short version" of the song, etc.?
So creating a Style doesn't offer the no-muss-no-fuss solution of spontaneously choosing the starting and ending points of a portion of a song and then looping it for an arbitrary length of time.
As far as copying-and-pasting in a DAW, that's also dependent on looping a predetermined section of the song, not to mention playing the loop for a predetermined number of iterations.