While I 100% agree that cosmetics in general (dreaming city, last wish, and gambit) need a much higher drop rate I'd like to point out that 3 chances per shattered throne once every 3 weeks is the same as doing 1 ascendant challenge a week for 3 weeks so you still have the same amount of chances at the drop.

Also the ship can drop from more than just the Shattered Throne, that's just where it has the highest chance to drop from. I've heard people say they've gotten the ship from the weekly ascendant chests, blind well, and the ascendant challenge. I'd imagine you can also get it from public events, normal chests, and the weekly story... Pretty much anything that drops dreaming city loot can drop the ship but the chances are just insanely low.

Again though, I agree the cosmetic drop rates need a significant boost.