Those weapons are still all being developed and would be brought out in any actually existential war where they seemed useful. The agreements would last only as long as the wars were not existential, or as long as the various countries involved believed that use of them, and the resulting retaliation in kind, would be more destructive than not using them. But one way or another, countries still develop them.
I don't think it needs to be a binary to be effective. Yes, those weapons still exist, but understanding of existential risk and political pressures have slowed them considerably and resulted in a safer, more cautious world.