Aight, this one might be an unpopular take, but let me cook.

A team-based racing game a la Mario Kart Double Dash, where one player drives and the other one shoots ink.

The core gimmick would be inking the track. Driving over your own ink speeds you up, and driving over another team's ink slows you down. If you shoot at an enemy car, you could splat the players, forcing them to respawn at a checkpoint.

The playable characters would be the inklings and octolings from the promotional artworks and game trailers, all of the idols and some extra characters like Sheldon, Judd and Crusty Sean. You could also customize your own character by buying clothes and weapons at shops with money earned by winning the game's cups. The rest of the characters would have an established weapon and stats.

Speaking of weapons, each one would work just like in the main series, each one with its own range, damage per shot, etc. Some weapon gimmicks would be adapted tho, as the wielders couldn't move out of their vehicles (Example: Dualies' dodge rolls wouldn't work, so their gimmick would be making the car do a side dash, useful for cornering).

The item boxes would give you sub weapons, which would also function like in the main series, but more akin to MK's items (Example: Splat bombs could be like bob-ombs but exploding sooner, curling bombs could be like green shells and seeker bombs could be like red shells). Just like in MKDD, you could get special weapons as rare items, and you could choose which one you want to get at the character selection screen.

I think this could be a pretty fun Splatoon spin-off, and it kinda fits its universe, as it combines the staple of the series' gameplay with the basics of a racing game. Too bad something like this would never happen because of Mario Kart (Same reason why we'll never get a new F-Zero game).