Quite simply, dragons need to be given controls for moving along their Z-axis. That is, they can currently move forward, backward, left, and right; they need to also be able to move up and down. Not simply look up and move forward, but move "vertically" relative to their orientation.
There are a couple reasons this is required. First is the obvious, functionality. If a creature/machine/whatever can hover, then it can also move vertically (helicopters and hummingbirds would be the most obvious real examples). Being able to hold its vertical position MUST mean that it is also able to
change its vertical position, as it is already constantly moving upward to fight gravity.
Second is consistency with the chosen fiction: dragons. Take a look at any dragon in any work of fiction - book, movie, or game. I cannot think of a single one (besides Dragon Commander and Divinity 2, both from Larian) where the dragon is hamstringed by not being able to perform vertical movement (taking off vertically, for example). Specifically, Draken: Order of the Flame is the best dragon-controlling game prior to this one (in my opinion), and it has vertical movement.
Simply, though, not being able to move upward and downward without looking at the sky or ground is honestly rather annoying. It's actually the reason that I haven't played Dragon Commander since it released, and the reason I stopped playing Divinity 2 a little while after becoming a dragon. The lack of this simple functionality is just... too much, and that's saying a lot, considering that I regularly play games that are 10-15 years old.
I love your games, but please, add this functionality. You added inverted Y-axis movement to Divinity 2, which is awesome, and I thank you. How about this?

Note: I apologize for the slightly rude tone this post originally had. I've been rather stressed lately, and that came out in my message. So again, I apologize.