Example: If the pump can create 5GPM of flow and you have the
washer in rinse so that the relief valve is not activated then your
4GPM supply is not adequate for the rinsing stage. If the same 5GPM
pump is dumping most of the volume over the relief as it is when you
are power washing then you are only drawing about 1GPM from a 4GPM
supply so that during this power washing stage the supply suddenly
becomes adequate.

SNIP
You have a funny way of looking at things--Let me change your example around
just a bit. You have a free flow of 5 GPM and a pump that can put out 4
GPM. No problem it works just fine. Now increase the discharge resistance
such that the pump operates on its relief valve. The flow out of the pump
will drop to almost zero or slightly above zero.

I agree.

In your example the pump will most certainly be in cavitation when not on
the relief valve, producing no flow

I disagree.The pump will cavitate but will still pump water.

, but when on the RV produces an output
of about 1 GPM. From your point of view, this suddenly qualifies as adequate
supply. I guess 1 GPM is better than nothing.

The 1GPM is not the adequate supply. When the power washer outputs
just 1GPM then the 4GPM supply is adequate during this time period.

Why in cavitation--assuming a 50 psi supply pressure and a free flow of 4
GPM--- AT 5 GPM (pump demand) the inlet line pressure drop would be
approximately 75 psi (25% increase in flow requires 50% increase in pressure
drop).

It doesn't work that way. When the water is flowing into the pump you
do not have 50psi. Furthermore you can't subtract 50psi by75psi. That
would give you a negative 25psi. There is no such thing.

The only force that puts water into the inlet of the pump is the
atmospheric pressure. At sea level you have about 14.7 psi maximum
to work with but this number will never be nullified by any consumer
power washer pump. At best you may be able to reduce the 14.7 psi to
9 or 10 so that you would have an effective atmospheric force of 5psi
that would create flow into the pump.

Note: The above method of creating flow is not the recommended way
for power washers.

The pump will not work, it'll just screech itself to death.
I have a power washer, as you must also have, and it works just fine, so
obviously, my house supply more than meets the flow requirements of the
washer.
MLD
Even when a pump is screeching (cavitating) it will still pump.