They actually are very much like aircraft carriers: Dragons are supremely effective against everything on the battlefield or ocean, except some very specialized counter-weapons, in this case ballista.
Their flames can burn/melt castles and navies with ease. They can eliminate unlimited numbers of troops, armor, cavalry, catapults, bridges, supply houses, grain fields, etc. If your enemy has them, your conventional forces have no chance.
Dany's dragon was hit with spears only because it needed to land in a stationary place and rescue her. That won't happen on the battlefield. Maybe they could sneak up on resting dragons with a few ballista wagons, but this seems unlikely. Especially since they prefer lofty aeries when they land.
While they are moving, they are nearly impossible to hit. In order to hit a flying dragon with a ballista you've got essentially two options:
1. Mount it on a 2-axis turret that can be rotated quickly enough to adjust for the dragon's jerky flying movements. Pretty unlikely, given the technology of the day.
2. Have enough ballistae firing so that the dragon cannot evade the fusillade.
Your crossbow shot then needs to hit a single point on the dragon, while not first getting hit by a big splash of dragon fire coming back at you. You've also got to do this while avoiding the two other dragons that are circling around behind and raining down fire on you.
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