Why use Toxins. When you could just Nuke the nest.

Given what we saw in the movie, firebombing them worked great, gunning them down did the trick(Pratt was soloing them), helicopter blades turned them into yellow soup, and Dan and his dad pretty much ended the queen with nothing but a 50 Cal and a pick axe. These things were by no means unkillable.

I was thinking that too. Secrets to intergalactic space travel were on that ship. Would have been nice to salvage it just in case the aliens that brought them here the first time ever decide to come back. Although it was in russia, so probably better to just blow the ship to pieces.

This I also don't understand. If I were the any government (especially Russia and the US), I would do my best to get any chance on grabbing it. This would then also had make a MUCH MUCH better excuse for the final act. It is ridiculous that neither the russian or US gov is not at least checking what the guy says, who brought back a toxin to kill the aliens. As said, alone for the potential tech on board. And this would be then the excuse for Pratt and his friends to go their alone fast, as they noticed that the govs are not interested in killing the aliens, but instead just greedy for the alien tech/weaponizing the WS by themselves. So to not risk this immediate danger, they do this spec ops final act, rescuing the world.
Much more believable as the plot, that every country now just preparing for war against each other, as there is no hope for humankind. Which of course would also happen, but for sure every chance to prevent/contain this, would be taken and resolve the war situation at least a bit. Some already existing conflicts could be on the other hand already over the point of no return, especially India/Pakistan and China and their ever expanding borders.