Or simply have higher standard to consider that below average Bethsda game an RPG.
This. Can't think of anything else.

Dragon commander? i.e, be the dragon!

That's not how it works. People don't get to change genre definitions just because of their absurd/unrealistic standards. A game is part of a genre because of static, unchanging defining traits.

Anyways, I'm not gonna derail this further. The fact remains: Skyrim is an RPG, regardless of what people want to claim, and that is not debatable.

Kid, everything is debatable. Genres are abstract ideas used by peoples to classify thing, and such artificial. Not to mention that those defining traits of yours are arbitrarily chosen by people. For example, by dtgreen's criteria (if she didn't change it) Skyrim ain't RPG because you control your character like in action game; by my criteria it's an RPG, but that is irrelevant because by my criteria it's also boring mediocrity for which I have no desire of playing.

And to not derail it any further, if shouts count as breath attack or not is highly debatable. I could see it as yes, but according to OP, I could also see it as not.

Draconians in Dungeon Crawl Stone Soup get a breath attack during the game depending on the colour they get (red = flame breath, green = poison breath etc). The breath attack is totally under control of the player, the colour however is not.

The I of the Dragon

The game came out of my mind immediately. You're one of the three dragons, so ofc you can breath fire (or ice, acid), they are your basic abilities.

It's on GOG:
https://www.gog.com/game/the_i_of_the_dragon

Breath attacks are available in some Shin Megami Tensei games (and spinoffs). They are usable by specific demons. In some games, they are accessible to the main characters as well.

In Chrono Cross, there is a recruitable baby dragon. His breath attacks are performed in a clumsy/humorous fashion, given fact that he hasn't grown in into size of the dragons the player will encounter as foes.

There is a dragon that is recruitable in Suikoden 3. I think he does possess a fire-breathing attack, but his main use is to act as mount for his companion.

Dungeons of Dredmor, though I must say the "breath" part is just the description. There are a lot of weird skills and abilities in this game.