Why would you build a second Cocoon?

[Mirage]

So take Cocoon apart and lower it gently to the ground in pieces. You have weapons, you have tons of tools, you have hundreds of airships, this is not a hard process.

Use the Graviton Cores to keep it in the air. Don't give me this "incompatible power source stuff, Cocoon's power source was gone anyway, since that was the Fal'Cie. Whatever new power source they're using could have been put in the old Cocoon, that thing had tons of space in it.

Reinforce the pillar. They had five hundred years to think of a plan, and we've seen what they could do for construction in that time. Heck, a bulldozer of dirt a day would basically have Cocoon resting on a mountain long before the crystal pillar every collapsed.

Build a blast shell. While Cocoon is large, it's also mostly hollow. It's also not that far off the ground anymore. So it has a much lower mass than a standard moon, and would be accelerating for a much shorter time than an object falling from orbit. It's force wouldn't be much more than a nuke, and between force fields and earthworks, you could easily contain the majority of the damage.

Hope is more of an idealist than a realist? Or maybe he's just dumb? Either way he didn't think of any of these options, or we can assume for reasons unknown they didn't work.

Or the mysterious 3rd option: SE's writers were too dumb to think about it.