Dragon fire is like phasers from the star ship Enterprise. They have to maintain the fire to do enough damage.
Too bad they're not more balls of fire or like photon torpedoes, just launch a couple at each ship, retarget, launch again.
They may want to complement the dragon attacks with cannon and catapult shots of fire balls to take down Euron's fleet, which would have a hard time with fire coming from above as well as around the fleet.
BTW, the giant crossbow may or may not pierce the dragons but why wouldn't a hail of cannon fire from the ships have some effect on the dragons as well? It wouldn't be any easier to target those cannon balls than the giant arrows but you have better odds firing multiple weapons instead of one giant one.