Dragons should be rotational:
They should swap after 1 minute of not taking damage, and they should be imune to dmg until they do their first attack.
The respawn time would still be 6 minutes.
This way, you can stop the dragon from swapping to what the enemies want without having to overcommit and fight.
But this also lets the enemy team ambush you for trying so.
Not that getting the "wrong" dragon is a bad thing, but remember there's a limited number of elemental dragons you can get in a game, and often it's better to wait for the right one.