I know the days of Undertale meta are here and gone and I don't have a grand point to make here, I just think he's a great character. He's fun to interact with, and also he does a great job of fitting into Undertale as a thematic whole. So I’m gonna say a whole bunch of words about it. And at the end you will say "Yeah, I guess you're right, I guess he is pretty cool." and I will smile.
As with every read-heavy thing I think I should state that I don't think all of it is intentional but I do think all of it is there and that's what's important.
My thesis is that the weird recursion of fiction and Undertale's ploy to convince you the game world actually exists is fascinating, and I think Mettaton is integral to selling that.
Mettaton has a lot going on. Immediately, there's the standard Undertale arc loop of "this monster doesn't want to kill, but needs to if they are to be freed", but layered on top of that, there's examining the way that people interact with fiction and fictional characters, discussion of representation, the relationship between game content and game designer, progressing along the narrative of Frisk becoming accepted by monsters, versus the need for the monsters to be free, it's a lot to try and touch on so I'm gonna like. Poke at every one of those and not do them the justice they deserve.
So here goes.
The first thing you learn about Mettaton is that he's fake. Artificial. Specifically, a construct. Built by Dr. Alphys, to be a "human eradication robot". But monsters love him, so much that he's a TV star. He is the most popular, prestigious monster in the entire underground - his name is on everything as early as the Papyrus fight, where he dabs MTT-brand anime powder on himself. The thing I want to convey here is that he has a fandom. Everyone loves Mettaton. But Mettaton is notably not a humanoid character. He has arms and a wheel to roll around on but no face, he doesn't even get a talksprite like the other monsters. And he wants to kill you.
I don't think this is a very opaque thing - Mettaton's existence in this moment is analogous to every game character, since games were always built first as challenges to be overcome. But people found potential in the medium beyond that. It's like, meta. I dunno, I feel kinda like an ass writing this, but I also... don't think it's wrong, so it goes here anyway.
He wants to do it because Alphys can't - and Alphys can't do that because she spent too much time watching Frisk interact with monsters, peacefully, friendly, not dangerous. She cares about Frisk, a lot, and wants Frisk to succeed, after watching them on her monitor for so long. Or so you think! Neither Alphys nor Mettaton want to kill you - Alphys wants to be respected as the hero, and Mettaton just wants to make everyone happy. Be the star he, and everyone else, wants to be. This involves putting a baby through a lot of danger but it's controlled danger - Alphys was always at the wheel, it wasn't real. In this moment, Alphys is the person making super-difficult Mario Maker levels, that only she knows how to beat, so she could beat them for you and look cool. And her presenting non-stop threats, challenges, only to dispel them once they're done, it's outright rejected conceptually - doing this is a character flaw.
And in the last moments, when the player is done traversing the Core, and the reveal that Alphys was putting you in danger all along is a distant memory, Mettaton EX is revealed, and the most prominent feature of the EX form is his fuckin' sexy face, something to empathize with. Something to express with. Mettaton being true to himself as the star of the Underground has anthropomorphized him, quite literally.
And once Mettaton is revealed to be just as real as any other monster, it resolves the theme Mettaton set up - how do you engage with fictional characters, when those characters are almost unilaterally presented as a threat, even though the threat they may pose is entirely fabricated? And the answer is "have fun with it". Mettaton is also the last fight in which you have the opportunity to kill - after that, there's New Home, in which all the encounters drop backstory, and attempting to kill Asgore is how you progress.
If you don't kill Mettaton, the midpoint of the game, the act 2 "false high" is here: Frisk is accepted by monsterkind, accepted enough to learn the backstory of how things came to be. There are no more random encounters after the fight. But this does not resolve the conflict, the barrier still exists, and Frisk can't return home, and monsters remain trapped. The fight with Asgore is the turn into act 3 - the game can't finish here. Asgore is killed by Flowey, and Frisk is trapped in Flowey's nightmare world, and the act 3 twist, the shift in tension comes when Frisk's determination keeps Flowey from claiming their soul and convinces the other human souls to work with them. After this, the path through the True Lab opens, so that when it comes time again, the Chekhov's gun established in the end of the Mettaton fight - "all of monsterkind supports Frisk" - is paid off. Every single monster is here, because every single monster watched Frisk on TV, and had that same empathic reaction that Alphys did.
And I think that this is really a key part of how Undertale is the only game to date to get away with "These are real, living beings that you're killing.", because it taps into, but subtextually rejects, the idea that fictional characters are fictional.
This is kind of a phoned-in segment, but in the no-mercy run, Mettaton continues being a stand-in for all monsterkind, but this time it's a lot more... upsetting? Admittedly I don't engage with the no-mercy run content that much, I didn't even watch Let's Plays of it because it's just... unpleasant. So the facts may be off. But Mettaton NEO's role is to stop the no-mercy run in its tracks, by being an intimidating boss that baits the player into using their check action on the first turn, instead of killing him. If you fail to kill him on the first turn, you're booted to the Alphys lives neutral run. And Mettaton is more clearly allegorical here - real beings, unable to do anything beyond "get in your way" and hope that some of them get away.
I don't have much to say about the NEO fight other than it's good, because I would have to do a no mercy run and I just can't, dog. Can't.