If you want us to interpret that literally in the sense that no measurement is perfect (being subject to calibration error, quantization noise etc.) then indeed my response cannot refute this statement. But it is pretty clear that you don't mean perfect here but rather that you cannot measure the different currents with a single meter. If you don't understand how #11 refutes that then you need to look at #11 again.
With the third paragraph I have no argument and again point out that #11 did not address that paragraph.
With respect to the 4th paragraph the situation is the same as with the 2nd. If you don't understand how #11 refutes it you don't understand what #11 says.
Yes, you are using a single meter, from a Bill Of Materials line item standpoint. But yiou also add switches to your BOM. So you are usig 1 meter + 2 switches.
I guess you could say if you have two cars, you only need to buy 4 tires, if you switch tires from one car to the other car. In the practice, if you have 2 cars, buy 8 tires. Or if you have 4 tires, buy 1 car.
For some reason you try to equate two things.
Procedure A
Looking at a meter and read the value on the dislay.
Procedure B
(1) Look at meter, note value
(2) Switch
(3) Look at meter, note value
(4) Switch
(5) Look at meter, note value
(6) Calculate
It does not matter how easy step 6 is. It is the 6th step. I said you could not read the current total by looking at the meter.
Procedure A and Procedure B are not equal,.
From a real world stand point, I offer 2 posible solutions.
(1) Hook up the meter such that it reads only the 240 VAC current only. Depending what is on the 120 VAC legs, this might be an accecptle compromise. If the 120 VAC legs power pumps, relay coils, PIDs, etc, things whose current draw is known and more or less constant, knowing what those devices are drawing may or may not not be important.
(2) If he has the budget and panel space to add 2 switches, he probably has the budget and panel space to add 2 120 VAC meters. I see them on ebay at surprisingly reasonable prices. The existing meter is labeled 240 VAC. the 2 new meters are labeled Leg A & Leg B.
I think these are pracical solutions