I personally feel that the biggest problem with having Dovahkiin as a fighter is you'd be presenting a drastically narrow scope of the series.
As an RPG, ES has such a ridiculous breadth of customization options, weapons, equipment and playstyles that it'd be impossible to nail down complete representation of anything besides "Nord Swordsman with wyvern shouts". Heck, even the number of playable races in Skyrim eclipses the number of alt fighter slots - No matter what way you spin it,
someone is going to complain about not being able to play as an Imperial or Bosmer (and god forbid you to bring gender into the mix; I can already hear the cries of "I wanted X race to be male/female," (if they decide on a 50/50 split) or "why are they all male?")
The main point of contention I see, however, is the representative elements of his moveset. As stipulated above, current RPG characters such as Link, the FE fighters and Hero have a number of "bottlenecks" which allow them to still be highly representative of their characters despite Smash's limited move options (Hero having a move that brings up a random assortment of spells, Link's iconic arsenal changing very little between games, FE characters using their default Lord classes, etc.). When it comes to Dovahkiin, however, no such creativity restraint or bottleneck exists that can allow him to satisfy the majority of the ES community (and yes, you can argue till the cows come home that they should be happy with the Dragonborn's inclusion regardless, but that's never going to happen on the internet, at least in a widespread fashion).
What we'll most likely end up with is a Western Swordsman character who throws in an axe or dual-wielded swords into a couple of moves, has one or two ranged attacks in the form of either a cross/longbow or any number of random projectile staves/spells, and a whole collection of moves that other fighters can perform (seriously though, Unrelenting Force would more or less be Mario's FLUDD with a different visual effect), except they can be charged up and the Dragonborn shouts some kind of meme phrase prior to launching the attack. This severely de-values the variety of playstyles that are on offer in Skyrim:
- Why can't I play as my pickpocketing member of the Thieves Guild who dumped all their skill points into sneaking, speech and one-handed daggers?
- Why do I have to use Dragonbane as my primary weapon? I wanted to use Wabbajack.
- Why can't I summon any Creatures/Dragons/Undead monsters to my aid? There are plenty of shouts and magic-related skills/weapons that can do this, so there's no excuse as to why this isn't the case.
- Why is there only stuff from Skyrim in here? I wanted him to wield weapons/abilities from Oblivion/Morrowind!
I believe that TerminatorLOL put it best:
I would only accept the Dovahkiin if he was an Argonian werewolf necromancer like in my game.
Sure, the above statement was obviously made in jest, but there will no doubt be an endless amount of people decrying the Dragonborn's inclusion for the sole reason that it didn't turn out exactly/similarly to how they personally play the game. Contrast with the overwhelming majority of the Smash roster (Doom Slayer included), whose abilities are generally narrow enough in scope that their movesets can adequately portray how they play within their home series.
There's also the slight fact that the Dragonborn is from a game that, while infamous for the fact that Bethesda have been re-releasing it on enough platforms to rival Resident Evil 4, the game and character itself are due to be overtaken by whoever is to become the next Protagonist in Elder Scrolls 6. Sure, Dovahkiin could simply be a marketing ploy by Bethesda to promote ES6 on Switch, but the Slayer already has the Dragonborn beat in that department by miles (in that it wouldn't make sense to promote your next game by using the main character from the previous game that will likely have little to no bearing on said next game).