So, here's what I'd like to see become of Splatfest.
[stuff]
BOOM! No more Ketchup on Ketchup for 95% of the Splatfest! No more guessing that the other team just had way more better players...
What do you think? Helps? Hurts?
I get where you're coming from with this, but to be frank going to a system like all of this sounds like it would only serve to create or reintroduce problems with the fest that have already been corrected up to now, all in the service of trying to resolve one issue that really shouldn't be as big a deal as people are making it out to be.
At its core, the Splatfest is meant to be an event where everybody picks from one of two sides, then bands together with their like-minded folk in a competition between the two things, but it's also a celebration of both sides and a big show put on for overall inkling culture. It's why you see the big rise of not-Miiverse posts and have all the extra squids dancing in the square and all. Separating the teams competing from the side of the debate they're voting for defeats the point of voting at all, doubly so if you still offer a snail reward to the most popular team (since, in that case, if you know one side is going to be more popular, why would anybody bother choosing the lesser at all?). Without the two sides competing directly against each other the entire rest of the event kind of falls apart.
Secondly, splatfests in Splatoon 2 already offer one big advantage over those in the first game: the ability to directly form a team with your friends and play as a group together. The entirety of splatfests in S1 was a solo experience unless you got really lucky with timely matchmaking, and pairing up is one of the things that everybody bitched and moaned about, so now it's here, but your proposal would immediately dash that away again in favor of randomly assigning people to battle-groups, and just before they start actually taking part in the event, to boot. In that case, you're just fighting alone with groups of random people, against other groups of random people, fighting for an arbitrarily-assigned team that you have no actual personal investment in. At least if you're playing solo right now, you're still fighting for something that you personally pledged support for.
Third, splitting into four teams instead of two only further confuses how you're handling scoring. How do you go about matchmaking to ensure that you get a fairly even spread against each of the other three teams? For that matter, if team selection is determined by the game just before the splatfest begins, how can you ensure that there are enough people active at a given time of day to actually represent all four teams? One team could wind up under-represented at some point out of sheer coincidence of who's online, populations could possibly vary even more than they already do if you're trying to form four groups instead of just two.
The complaints about the less popular team having "a better chance to group high-skilled players together" used to perhaps make a bit of sense in the Splatfest's earlier days, but I can't buy into that so much anymore once they started implementing their power-rankings-based matchmaking into things, and this time around they even took on the ranked mode's strategy of reforming teams after every solo round, so you're not likely to form up a good consistent group and start stomping on random newly-constructed opponents. If someone's good, then their rating will reflect it, and they'll be grouped with other players around their level, matched against other players of their level. The character of who makes up each team isn't as relevant as it used to be, since matches against each other will always be roughly more even now than they ever were in the past.
I get it that Ketchup people might feel a little short-changed in playing largely against other Ketchup people, but that's more a fault of the two sides Nintendo chose to pit together in this, not a fundamental problem with Splatfest itself. Mirror matches still count towards your progression up the ranks, so they still help you in getting those sweet sweet snails, and it really doesn't hurt the team in any way either. Just play the game and enjoy it as best you can, this kind of salt and calls for rule changes seem to come from the losing team almost literally every 'fest.
If there's one suggestion I would make to improve splatfests, and this is something I've proposed for a long time, it would be to adjust point-gains to that the difference in time taken to reach king/queen between players isn't quite so vast as it is now. Players who tend to lose more than they win in the current system can take two to three times longer to reach the highest ranks than winning players do, and while I get the incentive to play well, that's kind of motivation-crushing if you go on a bad streak. A really good run means you can reach your max rank in 2 hours or so, a really bad run can mean 4+ and that kind of a grind is rough to look at, especially for as precious of a resource as snails are this time around.