That would be hopelessly naive then. We do not have a 'world government', every government has complete autonomy on how they deal with healthcare issues, something that I believed to be well known. That's why each government has their own ministry of health and their own way of dealing with health insurance, budgets and so on. The degree to which these things are organized is impressive but in the end if the WHO publishes a guideline you'd be stupid to ignore it but you can if you want. And plenty of countries did.
And no, it should not result in a decline of trust in the WHO who clearly advocated for moving as fast as possible while governments the world over with some very rare exceptions took a 'let's wait and see' approach. If anything it should reduce the confidence that you can solve global issues with local policies.
Welp, that's probably not what people thought about the WHO before Covid, and certainly justifies the decline in trust. Maybe they could rebrand as World Health And Politics Organization.