I feel like a lot of people are saying "just because it was in xi doesn't mean it has to be in xiv", but why does that mean that it should necessarily be excluded from 14? I think wyverns are awesome pets and should be in xiv for no other reason than that.
That having been said, I don't think that drg should be the job that gets it simply because it's already an established job. Personally, I would enjoy seeing a wyvern-based job added to the lancer class.
Simply copy and pasting a class from another game is kind of like copying Lightning from XIII and putting her in 14. It feels fake; like she/it doesn't belong. Now I am sure they can spin a story to make it work, but you have to really look at what you're asking/wanting.
Is it that you are asking for a pet class? Because everyone is getting a combat Chocobo that they can use and base its abilities off what you're lacking. Sure you'll likely be in the 30s before you unlock it, but every class will be capable of having this adventuring companion.
I'm going to assume with you want a pet based class that has a Dragon/Dragon Sub-type as a pet. The issue at hand with building a class around a pet(s) is they'll typically either be too powerful because you can funnel health into them indefinitely, or the pets die in every real fight because of positioning problems, or that their strength is greatly reduced to allow for a stronger PC with the end result being they end up useless.
I think if you're looking for a pet-based class focused around a dragon, you'd be best off building feedback towards the next expansion... You could take something new like "Child of Bahamut" and start looking at how you could make something fit in the world of 14.
WoW Blackhand-US-Date of Retirement: 9/21/2010... /Sigh
Devari - 90 Rogue 85 DK Druid/Mage/Warrior 70+
FFXI - Shiva "Retired.... Or not? One more try, honest."
Desmar - 65 Sam 36 Mnk 18 Thf 12 War
FFXIV - Devari Garamond - Sargatanas 50 Paladin / Culinarian / Weaver / Armorer
Beta - Devaria Ariadne - Ultros - Pugilist