This was going to be just a comment, but I'm going to put it in the answer space & take the downvotes like a grown-up ;)
If you want the cynical answer, it's because there's so little actual excitement in the music itself that they have to do something to fill the stage.
The material is identi-kit formulaic post-Stock, Aitken, Waterman that still seems to be churned out with little change 30 years later.
There are no visible musicians, just a bunch of fairly underwhelming singers banging along in unison. So, they dance to hide the fact there's nothing else interesting going on.
Guaranteed to fool the average pre-pubescent.
There's was no way I was going to watch it all, just a bit of each. The ones where there's actually some decent block BVs going on are mimed - go figure. I wonder who laid those down?
Lifting a couple of comments to the answer, as this seems to have picked up more attention than I initially envisaged…
"it seems to put the entirety of Korean Pop in the same basket"
Not to be jingoistic - I'm putting the entirety of pop in this basket. Pop has always been formulaic, but at least the formula used to change every few years. We have now been through 30 years with so little change that it long ago became tiresome. There are occasional bright points in this otherwise bland, grey landscape, but this type of stuff is not it. You could dial back 20 years & find something almost indistinguishable, from any country. Hence my post-SAW comment in the answer.
Q: Can you elaborate please? 1. "identi-kit formulaic post-Stock, Aitken, Waterman" Who are these people? How's Girl Generation's music similar to theirs? 2. Why do you find these girls "fairly underwhelming singers"? 3. "Guaranteed to fool the average pre-pubescent." How so? I see many adults in the audience. 4. "block BVs" What are these?
A: 1.SAW were one of the biggest writing/production teams in the UK, late 80s onwards. They developed a 'hit factory' style of writing & production. Stock Aitken Waterman. 2. they really don't seem to be able to sing well at all in the live tracks, very poor. 3. Young kids are not very discerning. The adults will be parents. 4. BVs are backing vocals. block means a lot of them. Compared to the live versions, the mimed versions are very polished - more than hinting that the visible performers had little to do with the actual records. It wouldn't be the first time… by a long way.
And, don't get me wrong, I have nothing whatsoever against Stock Aitken & Waterman. They found a style & a way of working that was really very clever. A modern version of Tin Pan Alley, with in-house everything. All they needed to do was bring in the right singer for each song - sometimes several artists would record vocals over the same track, then someone would choose the best [I guess, I never saw their actual working method on that].
A bit of background, for those of you who don't know me.
I used to work with Pete Waterman, also Phil Harding & Ian Curnow, who were a part of the team, before SAW was fully formed. I was actually in the studio upstairs at the Marquee recording something [a total non-hit, don't even ask;) whilst Pete was recording You Spin Me Round downstairs. I did get to visit "the Hit Factory", PWL studios before it was fully finished. The offices & small studios upstairs were finished, studio 1 downstairs was a building site with a table-tennis table in the middle of it. I never saw it finished.
My point is - they did this more than 30 years ago!