Instead of ships being just another display piece, would it not be fun to fly your own ship, shooting down Fallen or Cabal ships or just other guardians in general.
To include all ships, there must be some form of a balanced fighting method like adding upgrades to your ship like "Quick evade" or "Temporary cloak" adding up to a limited number of possible upgrades that can be interchanged and found as rewards in various activities.
Maybe there could be an entire inventory holding Armor plating, weapon perks, decals and specialty perks!