I think many of the people who say that Snake doesn't fit in Smash have clearly never played a Metal Gear game. Sure he's a grizzled professional soldier, but in many ways, he's a parody or pastiche of that archetype, and he has loads more personality than the generic army men so common in a lot of games these days. Furthermore, Metal Gear Solid is a big reason why that archetype became such a popular one for game protagonists in the first place, making Snake not just a grizzled professional soldier, but THE grizzled professional soldier. The fact that his character became the model for so many other protagonists just goes to show that he's one of the most iconic video game characters of all time, period. Absolutely on par with Mario, Sonic, Megaman, and Pac-Man. He's consistently appeared in popularity polls ranked near and often above iconic Nintendo characters like Link and Mario, in both Japan and the US. His series has moved the medium forward time and time again in terms of what's possible from both a storytelling and gameplay perspective. He certainly owes a lot to Hollywood action heroes, but no more than Link owes a lot to fantasy protagonists or Captain Falcon owes a lot to Super Sentai shows.
I also get the sense that a lot of people who aren't very familiar with the series or character outside of Brawl think that the Metal Gear games are just straight-faced military themed games, not realizing that the Metal Gear series is just as goofy and eccentric as Mario and Zelda, if not more so in many cases. Sure, it deals with some mature subject matter, and has a particularly nuanced take on the nature of war, but always alongside robot ninjas and recurring characters whose primary trait is chronic diarrhea. Even the latest grimdark Keifer Sutherland voiced outing, despite incorporating themes of torture, war ****, mutilation, child soldiers, and how revenge slowly corrupts those who seek it at any cost, nonetheless features a mechanic where you can abduct wild animals using a helium balloon, and horses that **** at random intervals while you ride them. The major antagonist's name is "Skull Face". The plot still prominently features a giant mech that shoots nukes. You know, the ridiculous and contrived anime-esque plot point that the entire series is named after. The silly and over the top elements of the series easily outnumber the more serious aspects. Even in its darkest entries, Metal Gear maintains a tone and atmosphere that keeps it lighthearted and fun. It's a comic book version of the real world. And while this "real world" setting makes its themes hit a bit closer to home, I don't think any of the themes themselves (at least before MGSV) are really that much darker than similar themes that Metroid or Fire Emblem have explored.
I think Snake fits perfectly. He brings something totally unique to the table in terms of his design, but in a way that complements the other characters rather than feeling totally jarring, at least in my opinion, and he hails from a series that is just as "Nintendo-esque" as Megaman or Sonic when examined closely. Sure, he's a realistic human, but so are a number of other Smash characters who never get accused of being out of place. This is also a series that features character diversity as one of its greatest strengths, and saying a character feels "out of place" in a game where that's kind of the entire point just feels like a meaningless justification for not liking the character. Does Game and Watch feel out of place? Do Miis? Everyone is out of place. This is a crossover fighting game.
