The novice thermostat control idea.

Yes. Thermostats work in parallel. The simple answer that misleads you. It wins your point without telling why you don't want it that way. It's the however that getcha.

If the downstairs becomes too warm, then the downstairs thermostat turns on the AC by closing contacts in the thermostat - dandy.

HERE's the BUT ...
If the upstairs becomes too warm, the upstairs thermostat closes, which will make the downstairs too cool. As you have only one system, each time, the units feed the same air to the same places, the downstairs becomes colder than you want when the upstairs thermostat calls for cooling, so you have to set the upstairs thermostat higher, which negates the reason for having it there in cooling if you don't want downstairs too cool.

Same in heating when in parallel. If the upstairs becomes too warm, then the upstairs thermostat contacts open. When the downstairs becomes too cool, the thermostat closes, turning on the heat, which overheats the upstairs. By then, the upstairs themostat contacts are open, which makes it useless. The only time it would be useful is at night in bed upstairs when you don't care if the downstairs is cooler, or if the downstairs thermostat fails, preventing freezing.

When in parallel, any of the thermostats opens and closes to control the unit independently; so your idea to control the cooling from each floor with each thermostat WIRED IN PARALLEL doesn't work. So you have to be wary of SIMPLE ANSWERS that win points by deceptive simplicity. No matter what you WANT them to do, machines like thermostats only do one task as machines at the location they are in, not like office workers who are assigned to run around and compensate for somewhere else, so the boss doesn't have to know or listen to what's going on - he just gets his way.

Will it work in SERIES - NO. Each thermostat then acts in a chain so either one can turn off the machine; but it can't start the machine until the other one has its contacts also closed at the same time. In cooling when the downstairs gets cool enough the contacts open making the upstairs thermostat actions useless. When in heating, the upstairs gets warm, opens its contacts making the downstairs thermostat useless, so the thermostat can't make the downstairs warm enough..

The answer is expensive brand-new ductwork to allow single-stage equipment to move enough air when dampers close to a floor, or multi-stage furnaces and AC or, INDEPENDENT systems for each floor, especially independent AC control with zoned chilled and hot water on each floor as in commercial buildings..