We have enough nuclear weapons to kill off humanity. They have not been used because of fear of retaliation, the number has been reduced because of costs. But the US with it's largest conventional military would benefit from a removal of all nuclear weapons.

We'll see if Russia uses a tactical nuke when Ukraine enters Crimea.

Biological weapons have been killed because they are hard to be used operationally. You don't want to kill civilians, this creates more resistance (shown in WW2 and Iraq for example), also if you conquer a country you need people to run it. Biological weapons are not that useful.

> We have enough nuclear weapons to kill off humanity.

Humanity yes, mankind I'm not so sure. Earth is huge. There are a lot of humans. Some will survive winter. Some will survive mutations. Some will continue to reproduce.

Biological weapons also have the distinct problem of control: you can release them, but you can't stop them afterward. So, you need to be able to keep your own people safe from the release, which means expensive vaccinations across your population. And how do you test that your vaccination works? Or that it'll still work after your bioweapon mutates?

Bioweapons are useless unless your goal is to kill off everyone.

Modern chemical weapons are a better example of a thing we've banned.

But they were banned because of the consequences on their extreme use on the battlefield, not because were controversial before use.