Dragoon lore in FFXIV is entirely different from FFXI.

They get their powers from dragonkin; however, that does not mean the two fight alongside one another. Dragoons and Dragons, in Eorzea, are mortal enemies. If I'm wrong, then why does Nidhogg reportedly re-awaken to try and wipe Ishgard off the map every 20-30 years?

As Alberic states, Dragoons derive their power from their dragonkin counterparts; however, he also states that relying too much on that source of power will cause the dragoon to succumb to it, and be controlled by it's will. Estinien does this with Cloudwine. He is so hellbent on revenge that he fails to realize he has fallen under the dragon's sway, Nidhogg included. Basically, his desires for vengeance cause him to lose control; that's why he fights alongside Cloudwine.

And when he grovels to the wyrmgod for more power, his life is taken.

The lore is different, and they aren't going to rewrite it just so Dragoon can have a useless pet. There was never a lot of gear dedicated to making your 'partner' as powerful as he could be, and the 2hr was so useless they simply replaced it with a 'eat your wyvern and buff up!' ability, and apparently that doesn't bother a great many people.

No to wyverns. I like being a dragonslayer instead.