Countries like Singapore, Taiwan, New Zealand, and South Korea suggest that with sufficient planning and political will, there were alternative outcomes available compared to what happened in the US and Europe.

No it has not happened universally around the world, some countries only had the initial shutdown in April 2020 and then the schools were open again.

See here https://covid19.uis.unesco.org/global-monitoring-school-clos... France and Switzerland as an example.