I feel the criticism against FE in Smash have been oversimplified to "Too many anime sword users".
Let's break that down.
The biggest complaint is that FE is over-represented in Smash, sitting at 7 characters, the third most represented series overall, beneath Mario and Pokemon. While it is a long-running series, no doubt, it has by no means always been as popular or comercially successful as it is now. Awakening was when the series really hit commercial success and mainstream popularity, as well as being the first time the series sold over 1 million copies.
None of those things are inherently bad or problematic. Things become problematic when you take a look at other big name Nintendo franchises. Other long running game franchises who regularly push 1 million to multi-million sales, such as DKC, Kirby, Star Fox, and Metroid all only had 2-3 characters during Smash 4, compared to FE's 6. Not too mention there are plenty of fan favorite and very viable fighters from each of those franchises.
This becomes doubly frustrating when you take into account all of the other beloved niche games that have no characters in Smash, such as Advance Wars, Golden Sun, Chibi Robo, etc. Fire Emblem was no different from those franchises when it was added to Melee, and has since received a massive push because of it. Why can't any of those game receive the same chance, instead of adding a 6th, 7th, or 8th FE character?
The other main criticism of FE is that too many of the characters are too similar. Yes, many of the popular characters use swords, but the games are built around the weapon triangle of sword, axe, lance.
Imagine if the only Pokemon ever added were all Electric typed? Imagine that the Pokemon line-up for Smash was as follows:
Pikachu, Pichu, Pachirisu, Dedenne, Emolga, Jolteon, and Ampharos
It's boring when you consider all of the unused Pokemon types not being used. Not too mention that 5 of them are basically just Pikachu. Sure Emolga has a few unique moves that makes it a little different, but it's basically just a flying Pikachu.
That is why everyone is sick of FE. Robin and Corrin are the only unique characters from an aesthetic and moveset standpoint. We should be asking why of 7 FE characters, none use an axe or a lance, and why so many of them look and play like Marth?
At the end of the day, the criticism of FE in Smash may be tired and said too many times, but it doesn't make them any less valid.
Well put.
To expand a bit, let's not understate the fact that Fire Emblem has the third most characters of any franchise. It's only beaten by Mario and Pokémon, which are the best selling game franchise in history and the most profitable media franchise of all time, respectively.
Legend of Zelda, one of the most famous and venerable franchises since the early days of video games, has less characters, despite there being several characters like Skull Kid, Midna, Zant, etc. that have a lot of potential. Arguably, the series hasn't gotten any newcomers since Melee (given that Toon Link is more or less a tweaked Young Link). Fire Emblem's gotten several.
Donkey Kong, Metroid, Star Fox, and Kirby also didn't get any new characters in Smash 4, when Fire Emblem got two newcomers and an Echo Fighter, along with Roy getting added back.
Many of Fire Emblem's characters were added just a few years after their respective games, or sometimes even before. Roy was added to Melee before his game was even released. Corrin was added to Smash 4 before his game was released internationally. Meanwhile, characters from franchises/games that are much older have been neglected.
And people still ask for more Fire Emblem characters.
So it's not just the volume, but the amount of favoritism obviously being shown to the franchise over so many other franchises. It gets more love than some of the most historic franchises in gaming, primarily just because of one game from 2012. Sakurai also admitted in his most recent Famitsu column that someone on the audio team really loves Fire Emblem, so even its music will be getting a lot of attention.
There's also the aesthetic issue. Fire Emblem has always had an anime aesthetic, and with Awakening, it leaned heavily into a lot of anime tropes, hence its boost in popularity. Most other Nintendo franchises are more unique in their aesthetics, thus most other potential characters would add more aesthetic diversity to the cast (e.g. a big space dragon or a big crown-and-cape-wearing crocodile), but Fire Emblem characters all draw from the same basic anime art style. Hence the label "anime swordfighter" that's been given to Fire Emblem and other franchises. That's why a lot of people were excited about Simon Belmont's appearance, because he's got more of an 80's "Conan the Barbarian" look, and he uses a whip instead of a sword, so he adds a lot to the cast.
Do some people take their resentment too far? Of course. Fire Emblem has become a very popular franchise both in Japan and in the West following the release of Awakening. To say that it doesn't deserve attention is ridiculous. And the characters that are in the game are all genuinely loved by a decent number of people, as opposed to some desired characters like Waluigi, where most of the character's support is ironic. But when your representation is only beaten by the two biggest gaming series in history, then maybe that's a little much.
And when people have been asking for beloved and unique characters from other long-running franchises for over a decade, but we keep getting Fire Emblem characters from games that have only come out recently (or in some cases haven't even come out yet), it's not hard to understand why some people would be miffed.