The pressure in the cooling system is created by the rad cap and the fact that fluid(coolant and/or water) will expand in volume when heated.
As engine heats up the coolant expands in volume, and because lower rad hose is open this pressurizes the whole system even with t-stat closed.
The rad cap should hold in this pressure until it's pressure limit is reached, i.e. 12psi, 14psi, 16psi, ect.....
The PSI rating on the cap is set by manufacturer based on engine "hot spots", the point of pressurizing the cooling system is to raise the boiling point of the coolant above any "hot spots" that may occur in that engines design.
But the PSI also needs to stay low enough so hose material and connections don't need to be "high pressure" types and gaskets as well.
In your description it reads like you have a rad cap that has lost it's pressure rating, it is basically a 0psi cap.
As coolant heats up it expands and flows into the over flow tank as soon as 0.1psi is reached, coolant boiling point is 230degF at 0psi so at 195degF at t-stat any "hot spots" should be below 230degF, so no issues.
Most vehicles can operate fine with 0psi in cooling system, assuming 50/50 coolant is used, but under load, i.e. climbing a long grade, hauling a load or trailer, the engine can heat up more which is why pressure caps are used.
And yes, if rad cap was working at 14psi, for example, you would have a hard time squeezing the upper or lower hose, a basketball has 8psi of pressure, football 13psi
I would replace rad cap or have it tested.
And FYI, there are TWO valves on a rad cap.
The pressure valve has the big spring, this is the OUT valve, in the center of the OUT valve is the IN valve.
This smaller valve allows coolant to flow back into the rad from the overflow tank.
As the engine cools down the coolant shrinks, when the pressure in the cooling system reaches -0.1psi this small valve opens and coolant is sucked back into the rad from the overflow tank.
If this small valve fails you would see collapsed upper and even lower rad hoses, because pressure in cooling system is -10+psi after cooling down.
This can also be caused by overflow tank being clogged, coolant can flow in, but debris in the tank settles at the bottom and blocks flow back into the rad.
And squeezing the upper and lower hoses is a good way to check rad flow, once t-stat opens coolant can flow thru the rad from top to bottom, the lower hose will have a slightly lower temp(-15-20degF) and be only slightly softer to squeeze if flow is good.
If lower hose is alot cooler and very soft to squeeze then rad is getting clogged up, suction from water pump is making it softer and slow flow thru rad is cooling off the coolant more.