I can (potentially) imagine statting an unusual dragon as a fighter at my table. Usually I make them dragon sorcs, but a freakishly weird dragon might have spent all his time training physically and neglecting his innate magic... in which case, yes, this dragon has Action Surge and Extra Attack on his bite weapon. Ditto Extra Attack on his weapons when he shapeshifts into demihuman form.
He'd probably be a bit of a pariah among dragons though, given all the schmoozing with humans that he's presumably done to pick up weapons tricks. He's the dragon equivalent of a human who spends all his time hanging out with cows and sheep, or a crazy cat lady.
That's interesting. The different way people opt to use and treat things in RPGs is always a subject of fascination for me. I have to confess that I almost never give dragons class levels, or spellcasting abilities.
I have two primary homebrew worlds: Tenesia, and Wildwood.
In Tenesia, dragons are beasts. They are cunning, wicked creatures that hibernate for decades only to rise, shake off their slumber, gorge themselves on humanoids and animals, mate, and destroy everything they see as a potential threat to their territory. They cannot speak any formal language, but they are capable of learning to understand the languages of others. Being smart enough to understand worldly changes with the passage of time, they may eat or destroy all the settlements and fields within a day's flight of their lair just to prevent unwanted expansion near their lair before they wake again. These dragons are not greedy. They do not amass treasure hoards. However, many of them have learned that magic and metal are humanoids' greatest weapons against them, and they will seek to destroy or eliminate magic and metal when they see it. If a dragon knocks the roof off a building (or part of the roof) and sees books inside, it will burn the place to ashes so no spellbooks or scrolls can survive to be used against it. If that same dragon tears open a building and finds an anvil present, it will either melt it, hurl it into a nearby body of water (if present), or grab it and hurl it at buildings and people from a great height to turn their metal against them.
In Wildwood, dragons are manifestations of nature. Nature is the impersonal over-deity of that world, and those who don't keep the balance of nature earn her wrath. When a settlement has offended her dearly enough, she will send natural disasters to ruin and destroy them. Sometimes, these disasters are dragons. The dragons sleep within the forests, volcanoes, swamps, etc. and they rise only at nature's call, destroying those who've offended her before returning to their rest.