Older cars didn't have the situation where the radiator cap was not the high point in the system as is the case with the V6 hence air would move to the cap and be pushed out by fluid. as to how air gets in there without an obvious leak, those inlet manifold gaskets start to leak and instead of pulling liquid back from the overflow bottle they suck air in.
IF, (and I stress if) your theory of how air might get into the system is correct, then you've actually saying 'bleeding the system' is not a fix. At best its just diagnosing a VERY expensive repair. So expensive for most that its most likely they'll flick the car because they'll see it as not financially viable to throw that sort of money at a car of this age.
And the reason I say 'if' your theory is correct, I find in impossible to comprehend that if the intake manifolds are such a poor seal to allow air to re-enter the system as the engine cools to the point of a vacuum, then they would leak coolant like a sieve under the constant pressure of the cooling system at operating temperature.
The irony of 'air in the system' is that we've gone from starting with the simple and relatively inexpensive task of replacing the temperature sensor and thermostat to potentially junking the car due to the expense of a major repair.
I'm aware of why they put the bleeder where it is.
Still waiting for an explanation of how an air blockage in the cooling system results in the temperature rising and then suddenly and rapidly falling back to normal temperature, time after time. I believe it would create poor circulation and/or low coolant level so the engine will get hot, and just stay hot.
If the OP changes the temperature sensor, thermostat, replaces the coolant in the process if due, and in the process bleeds the cooling system and it works then everyone is happy. I'd certainly be doing a simple inexpensive task like this, total cost of about $40, before considering pulling the intake manifolds off.