Adding a back flow preventer or a check valve to a domestic water supply will create a closed system.
Usually the issue of thermal expansion in a close system is handled by installing an expansion tank on the cold water side of the water heater.
Could the thermal expansion in the system be handled by installing a pressure relief valve; with a relief pressure lower than the relief pressure of the T/PO valve of the water heater?
Of course this relief valve would dump a small amount of water every day...... approx the amount of expansion of the cold water heated to water heater temp.
Is the expansion tank solution "better" than the relief valve solution? or is a relief valve a better solution?
I'm just curious........... since I can see if the relief valve is working but the behavior of the expansion tank is internal & thus hidden.....so I have to go on faith as to whether the expansion tank is doing it's job.