OK. if there is something restricting the flow. Be it one of the cheap Pressure Regulators (That Valterra up-thread with the pressure gauge I am told is good but I've never tested it.. more later) like the 3/4" about cylinder types even if they are called "HIGH FLOW" or some other restriction like a partially clogged inlet screen or valve.. Then there is an "Air Cushion" in the water heater.
When water is OFF. the pressure in everything goes up to around 50 PSI. then when you first turn on the water the HOT tank can discharge back into the cold line. Normally not enough hot gets into the cold line for you to notice. But as the pressure in the HOT tank goes down... The flow slows since not enough water is entering the RV.
Now.. this should only happen on city water. not on "Tanked" water
What I did.. originally I used a WATTS 3/4" in-line regulator till it aged out then a ZURIN, also 3/4 inch (1/2 should do it but believe it or not would have cost more at least the ZURIN I put a gauge after the regulator and Turned on a major water sucker.
Cheap ones.. Watch the pressure go down
Cheap HIGH FLOW. Watch the pressure go down
Aged out Watts (I could not find a rebuild kit) Watch the pressure go down
Brand new Zurin.... Watched the needle sit there on 50 like it was glued.
Later. For other reasons.. I stopped worrying about pressure regulation on the city side. Filled the 80 gallon on board and pumped it out for everything. That worked great. and Solved a rare other issue (over chlorination of city water)