So we're basically asking why is everyone so effing stupid?
The copious amount of nuclear bombs is only a good idea if you don't plan to live on Earth any time soon. The largest Blue nests go deep into the ground (about 500 meters, judging by one of the diagrams), so an air burst isn't going to do the trick; you'll have to use a surface burst, which will pulverize all the tunnels and egg chambers...and leave a ton of nasty fallout (as opposed to the air burst, which produces no appreciable fallout). Now, if you do that with every Blue nest, you will kill them all, and probably cause a full-blown biosphere extinction. After that, humanity gets to wait for the Earth to detox (for the fallout to reach its half-life), and then for the biosphere to recover to the point where it can actually support human civilization again. This would likely take several thousand years. So yes, nuking the planet to the point of purging the biosphere might make you feel a little better, but now you end up stuck in space for a VERY long time and the whole point of nuking the Earth (namely to take it back) becomes moot.
Well yeah, but if you're stuck in space anyway...
Well yeah, and when the resources run out on space, the end.
The Mecha Designs, at least in the beginning of the series. Who thought it was a good idea to have a mecha with literally no protection for the pilot's head save for their helmet?
The cream of the crop is the two-man mecha, where one pilot handles movement, the other weapons. Sounds logical... except its weapons are its fists. Imagine being in a fistfight where your arms and legs are being controlled by two different people. Now imagine there's STILL not adequate pilot protection.