You're still thinking the old way. Once you put everyone on one time zone, you just have to remember what time midday ("noon") happens in a particular locale. Then, simple arithmetic will take care of the rest.
You can do the exact same mental calculation with time zones as they currently exist. Either you remember different business hours or different times zones, but in either case you have to remember something, because these categories exist for reasons of actual difference that cannot be papered over.
This is one of those recurring topics that generate endlessly circular arguments on Slashdot and lend credence to the notion that we're all aspies arguing over tomato or tamato.