Saying "everything will work out perfectly" is basically an engraved invitation for the opposite to happen.

But I'm not outright opposed to the idea; my preconceptions are heavily based on fiction in this case, which isn't exactly a strong foundation. I think we're morally obligated to try and save as many people as possible, especially if it can be done safely, but more information is definitely needed to be sure about that. It also still operates under the assumption that our worlds have in fact been destroyed and everyone in them is dead, which we don't actually have any evidence for.