The WHO has shown itself to be practically useless. The premise that sovereign nations need the WHO to cooperate is false. Diplomacy and cooperation between nations was the norm for many years prior to the WHO and will be the norm for many years after the WHO’s inevitable abandonment and demise.
Do you have a concrete example of public health cooperation amongst more than 2 nations before WWII? As far as I remember, every country just covered its metaphorical arse during the Spanish Flu pandemic, for example.
Of course, cooperation is always possible, but what would be the extent of cooperation between say China, Russia, and the US if a new treaty were signed today?