Does every military vehicle require an NCO or above as TC?

You won't find it in a regulation, it doesn't exist as an Army wide policy.
It will be in a local policy. Usually comes up after someone does something stupid and caused an injury or death.

Unit Specific SOP. When we have movements we only require one vic to have an NCOIC or OIC for each chalk. Other then that, they only need to be fully licensed on the vic they are a TC of.

Are you asking if one is required in every vehicle? Not in any unit that I served. Movements always had an Officer or Senior NCO as Convey/Movement Officer/NCO, but didn't have a vehicle commander for every vehicle.