......mainly due to the fact that the front of the motor is higher than the rear (when on level ground and air rises in a liquid) and running the motor naturally moves air upward and eventually out at the higher front of the motor, right? Once air exits the higher front of the motor it continues to rise to the bottle that is even higher than the front of the motor, right?

If I understand correctly, a closed cooling system starts "bleeding" air to the bottle the moment the motor is started. With an open cooling system, air migrates/rises to the rad cap but does not "bleed" out until cooling system pressure equals/exceeds the rad cap pressure rating. When the rad cap pressure rating is reached, the rad cap opens thus releasing/"bleeding" air/coolant to the bottle.

 

Check this out from the FSM

This system does not have a radiator pressure cap. Instead the pressure cap is mounted on the coolant pressure bottle. System coolant flows directly through a fully pressurized Hot-Type expansion bottle. Coolant flows through the pressure bottle at all times during engine operation whether the engine is cold or at normal operating temperatures.

Larger coolant volume caused by thermal expansion during engine operation is absorbed by the expansion chamber in the bottle. Air trapped in the system is purged through the pressure cap vent valve during maximum coolant expansion..

 

That's the beauty of a "closed" system.....if the motor is running, any air in the system constantly bleeds to the bottle, even when the bottle cap is on tight. Not so with an "open" system. Open system only bleeds air when the rad cap is off (can't drive with the cap off) or when the cap is on AND pressure equals/exceeds rad cap rating, thus forcing air to bleed past the cap. Obviously an "open" system will not bleed air when the motor is cold (unless the rad cap is off).

I still don't understand why "closed" cooling systems seem to get a bum wrap. There's too much to like about a "closed" cooling system over a "open" cooling system, IMHO.