I can't speak for the Korg's... I think the PA2 has them, not sure about PA1.
I don't know how Yamaha implement it, but Roland allow you to place markers on the fly, while it is playing, or play up to a point, pause, put in the marker and continue. You then 'save' the SMF and the markers are stored in the file.
As to disjointed jumping, it's not really a problem, as you would tend to put these at musical boundaries, start of a verse, or chorus, etc.. The Roland system has you press for the jump at any time in the bar, then it jumps at the end of the bar. Most songs will tend to have a fill or something similar leading up to the mark point. It can as easily go to a verse or a chorus, most of the time. I find it no mare jarring than many arranger fills that go from really busy variation 4 to very simple variation 1... Not perfect, but usually acceptable (at least in six or seven fill arrangers).
For the jazzers out there, or those with simple verse chorus song construction, there's another trick I use the M/J feature for.
I'll use the arranger to create a sequence from the style for a song where I do a whole verse and chorus at each of the variation levels (or head for the jazz tune), then use the Mark/Jump feature to chose on the fly where I want to take it, up or down in intensity. It's sort of a poor man's take on the Chord Sequencer feature, that would remember the chords, but allow you to use fills and variations freely. That feature is RIP, sadly, so at least the M/J's and a sequence give me that ability back, albeit a more limited form.
Other things the M/J's can do is allow a free 'vamp' in the middle of a tune, but only when you want it...
Simply leave say 16 bars empty at the end of the song, THEN add in the vamp bars. Now Mark/Jump at any point in the song to the vamp, and give yourself a Mark to a point you want to come back to. Now the sequence will play top to bottom without the vamp if you don't hit the Jump button. But if you want to extend, or do a voiceover, or a funky breakdown, those extra sections are ready to go if you are!
You can use Mark/Jumps on whole sequences... String four songs together (only four M/J points on a Roland, I think Wersi have more, but I think Yamaha do four as well. I wish there were as many as you wanted!) with plenty of gap between them (append one sequence to another). Put in markers after the intros. Now you can play song 1, and finish, or song 1 and Jump to song 2 as a medley, and finish, or Jump to songs 3 & 4 as medleys (at any time in the songs). A freeform medley, but done with SMF's instead of arranger mode! (And don't forget, you can hit 'transpose' during a Jump, even to a sequence).
The feature completely changes what sequences are capable of doing. Finally, the rote 'start to finish' form is GONE..!