10:50 Glow pikmin aren't tecnically pikmin if you see the piklopedia, they're more like some sort of ghost, so I doubt they’ll get one either. But if you really want to stretch it, the lumiknoll is kinda like their onion so it is still valid for your run!
Using 2 player mode, you can break the electric fence on the surface of SST and get the yellow onion before entering any cave. It's a bit slow to use just red and yellows through BA. If you get through to SS, climb the sand castle, build the wall and break the blue onion out of the ground using a bomb rock as mentioned or using 2 player mode. Since the ice onion is locked behind a cave which can only be entered by reds, it's a safe way to it (though a bit tedious due to the cold). For the second half of the game, the video explains everything with no strategy differences. TLDR: 2 player mode is OP
if you can, you can also use the pebble pitcher's ice blasts to destroy the hydro jelly in last frost. (that is if the 2nd player is able to use those before getting russ)
Re: what you said about ice pikmin and their combat effectiveness: different pikmin type have different damage values assigned to them. Blues and yellows do 10 damage, red and purples do 15, whites, pinks, and ices do 5 (rocks do 40, but it's offset by the fact they can't cling on to opponents and just rush into them at a much slower rate). Aside from rocks, all of them attack at the same rate. I'm guessing the perceived weakness of ice pikmin is because winged and white pikmin, you're probably not using in combat very much (unless it's sacrificing the white ones for poison damage) whereas ices are a mainstay. I'm guessing the lower attack power is to compensate for the freezing effect, which I'd argue is still overpowered, but that's a whole other discussion