This post is kinda old hat I do believe, but I toss in my two cents, since I remember it way when; Couldn't say anything when it was really on topic due to the fact my account was not up at the current time (and yes, I restarted. How I miss ye Besaid).

Dragoons through most of the Final Fantasy games have not had wyverns/dragons BUT there has always been a connection to Dragoons with Dragons. Sometimes good, sometimes bad. There was really it seemed two sides of the Dragoons. Those that slayed the Dragon to gain its power and those that worked with the dragons, learning from it.
However to say a Dragoon never teamed up with a Wyvern/Dragon is a lie in Final Fantasy History.

Lets start with Final Fantasy II -
Richard Highwind (Kain's adopted dad), used a Wyvern as a flying mount and worked with the Wyverns/Dragons. The term Dragoon here was used for those who were spear wielding individuals who rode on the backs of these beasts. In part of the story you actually go to the valley where the Wyverns are and you try to save one from dieing.

Final Fantasy III - Nothing special to note here outside of being your standard Dragoons.

Final Fantasy IV - Dragoon's get the Darkside / Holyside thing going on (by the time of After years), also becomes American's (I believe) first time seeing a Dragoon (Hi Kain), unaware that for a time he was connected to the dude in Final Fantasy II.

Final Fantasy V - The first time Lancet shows up, which if I remember right.. allows you to learn moves.

Final Fantasy VI - No Dragoon (BOOOO)

Final Fantasy VII - Cid Highwind, Not exactly a dragoon, but he moves like one.

Final Fantasy VIII - Ward Zabac, like Cid.

Final Fantasy IX - Freya Crescent, everyone' favorite rat gal if you were a fan of the Dragoons. So up until her, you hadn't seen a true dragoon since 5 really. It was about time the Dragoons came back and she came back with her own Lancet and when she kills a dragon, she gains their skills.
This represented in itself the first time people may have really gotten to see a Dragoon do such a thing, as I know 2 was not as popular as say 9. This is where you see the two sides of the Dragoons as well. Those that work with the Dragons and those that kill the Dragons to grow stronger.

Final Fantasy X - Kimahri is a blue mage, Dragoon hybrid kinda guy. (kinda what inspired my direct on FFXI when Blue Mages came out later).

Final Fantasy XI - The debate place. This is where you people are pointing at and going: "Remember that blue wyvern? We either love/hate it." (also the loldrg). They took the Final Fantasy II concept and gave it a minor twist. You had to go save the little Wyvern, some dude used it blood, and you had to slay him in order to prove that the Wyvern was not an evil creature.

Aaaand then we move into new formula Final Fantasy Games..
I'm also not going to get into Final Fantasy tactics.

So really, it mostly depends if the players want to go the Final Fantasy II direction, or a later Final Fantasy version. Perhaps maybe even both.

I always thought it would be interesting if Dragoon could have a sub group. You had those who worked with Dragons and those who were against the Dragons. Perhaps those that wanted to aid the dragons, got a wyvern which had to be raised, trained, and later as it leveled could also be used as a mount (if they ever allow us to control our own airships).

The other group didn't use wyverns, instead they relied on their own brute strength to get them through a fight. Maybe having access to things like Lancet or if they killed a dragon-type mob they gained a stat boost for a duration of a time.

In the end, I do love the Wyverns, but I am a massive dragon-fan on the side as well, but as this conversation goes. I just wanted to bring out the history of Dragoon onto the table, as it had yet to be done and from here, it really is up to the company what they believe is best for the game.