People call this the Super Smash Bros Melee of the Mario Kart franchise, & at the surface level there are some definitive similarities:

1. Strangely refined, simple yet perfectible mechanics for a rushed game
2. Meme status top tier to the point where everybody knows Funky Kong as the face of the game, a la Fox
3. Die hard fanbase, people who have modded the game to be far greater than its base vanilla form

But there are also some definitive differences between the fact that Mario Kart has a lot more fundamental randomness (namely in the item system), and that because it's not a fighting game, its not as upfront with its mechanical refinement.

All of the tech that makes this game special might not be apparent and might require looking up guides for nearly hidden things like wheelie chaining, spin drifting, slip drifting, etc. The game is also much more focused on micro-tech as I'll call it. Small little time saves will add up quickly and being able to execute really tight driving lines and clean mini turbos into wheelies to maximize time spent at topspeed is half the skill here. While other games might be more about "broad strokes", or big techniques or solutions that lead to an "aha" moment that allow you to beat challenges, racing games are special in that they force you to bunker down and slowly refine all the nuances and subtleties of your driving. This type of skill ceiling is what makes this game so special. The difference between a beginner and an advanced player is very wide, but not in a way that's incomprehensible from the beginner's perspective--the advanced player is just like a full refinement of that beginner in a way that is truly special to see.

Now, beyond all this praise, I'll lay out a few of the typical critiques of MKWii
1. There's only 1 viable character
2. The items are too powerful, which is diametrically opposed to everything you said about skill ceiling
3. Karts suck in a game based around karts
I would address the arguments thusly:
1. Funky kong is the undisputed top tier, but that doesn't stop daisy from also being an excellent choice, and there's even some niche usage with other characters. For instance, lightweight characters all have access to the magikruiser, which is the vehicle with the best offroad stat in the game. Beyond lightweights, baby luigi and baby daisy are seen as kneck and kneck due to their speed increase, but toadette also has good selection as she trades speed increase for offroad increase. Don't get this too twisted as me saying the balance in MKWii is genuinely good. But there's a little more interesting conversations in the mid tiers than initially given credit by the fact that funky kong is meme status.
2. Items are a vital staple of what makes races interesting. And while I will admit they stand somewhat against the idea of pure fundamentals based driving by injecting randomness, the randomness is played for in competitive oriented races like lounge. The shock is extremely powerful and there can only be 1 in play, so players literally race backwards in order to try and acquire the shock to support their teammates (being in a lower spot is a higher chance to get shock. This technique is called bagging). And finally, if you still just don't want to play with these mechanics, Time Trials and even Online Time Trials via mods is available.
3. Vehicle selection is sort of the same case as statement #1. The flame runner is undisputed best, holding almost all world records on time trials, but there is niche selection. For instance, daisy mach bike has tighter drift, which makes her more forgiving for beginners, or for playing on custom tracks where the turns can be less forgiving. Karts actually have held world records in the past, too. But even between just bikes, not all world records are set on the flame runner; Some tracks historically have taken advantage of the Spear, which has very weak drifts, but even higher top speed. And, for lightweights, the choice between bullet bike for better all-round stats vs magicruiser for the x-factor of high offroad is a genuinely interesting alternative playstyle for funky kong. But I will concede that yes, karts are bad, and there IS a clear indisupted Master of Everything for this game. I still don't think this is fundamentally a bad thing, but it's valid to form preferences in relation to this fact. This fact can be re-worded into a positive statement as well: Funky kong Flame runner is the most fun vehicle combination in any mario kart