With Pacman you're right that he's designed to emulate Pacman games, and that every character is designed with that sort of thought process to some extent or another. I cut the part of your post where you say every character needs to carry the character's essence when I quoted you because I have no disagreement there. I also mentioned that things ultimately have to work together as a cohesive playstyle. But what I was more getting at was you saying that characters are based on simple concepts like stat changer, puppeteer, ect.. The only concise way I could describe Pacman is that he is Pacman, which is neither an archetype nor is it simple, as there are multifaceted aspects to what makes Pacman Pacman, and in order to make that happen the devs had to get really creative with abstracting things from his games and then unabstracting them to fit the context. Archetype means an overarching type that a lot of examples fit into. Pacman isn't tailored to fit an archetype, he's tailored specifically to be Packman so hard that he doesn't fit into an archetype.
Furthermore, and towards my other point, that point can be reached not only by starting with a character concept and creating a moveset to fit that, but also by selecting moves peacemeal that represent different aspects of the character and then skillfully assembling them together into something that works. Example off the top of my head - Marth. All his moves have sweet spots to emulate crits in Fire Emblem. Dancing blade is a multi-step attack because FE has multi-attacks if you're fast enough. Counter is there because FE has counterattacks. Sheildbreaker is based off of Marth's signature weapon the rapier piercing armor. He's big on spacing because positioning is important in FE. Ect.. Sakurai took a bunch of unrelated concepts that happen to be important to Marth or Fire Emblem, converted those to even less obviously related individual character traits and moves for Smash, and then found a way to make it all work as one character. From a design perspective that's wildly different from something like taking Rosalina, saying "she'd make sense as a puppet character, let's try to make her moveset a puppeteer toolkit" and working from there. When fans make "a bunch of unrelated references" type movesets the Marth thing is what they're going for, it's just really hard to do well. In essence I'm objecting to the idea that you need to start with an overarching theme for the character and build things from there, when you can also represent different aspects with different moves or traits and then put them together in a way that works.
Corrin has several spacing tools and I even said if I had to I'd call them a zoning character, but they plays loose with the concept. I'll more or less cede the point there though.
With G&W the fact that his moveset is a bunch of random incongruous stuff is itself conceptually representative of the character. The G&W games are just a bunch of handheld games unrelated beyond hardware and publisher. Unlike everyone else in Smash G&W's games have no overarching gameplay concept, no consistent or even primary setting, characters, tone, style, nothing. And that's why none of G&W's moves have anything to do with each other either. But they are still put together in a way that the complete character works as a fighting game character. I'm not sure I'd say being fragile or high risk high reward is a "central idea" of G&W. It's certainly part of his character concept, but there's large chunks of who he is as a character that are unrelated to that. It's less central and more one of many pieces of the pie.