So from what I'm understanding, putting the connection between the potentiometer and the return would result in zero current going into the load when the tap is at the bottom of the potentiometer, which is not a good thing?
I tend to write choppy sentences when explaining things, so be patient with me please.
I'll try to keep to one thought per sentence.
I think this thought is more significant to your question :
whenever that connection IS there, you have division of current between lower portion of your measuring potentiometer and your meter.
As you pointed out, that's true regardless whether it's an ammeter or a voltmeter.
So the answer must lie in the difference between ammeters and voltmeters..
An ideal voltmeter draws zero current and a real one comes pretty close to ideal.
An ideal ammeter has zero voltage drop, a real one has small voltage drop and so do the real wires going to it..
So the division of current is negligible when you use a voltmeter,
But substantial when you use an ammeter. Worse, it varies with position of float.
So, if you use an ammeter you should remove that connection so ALL the current has to flow through your ammeter. That eliminates division of current.
That's a basic rule for measuring - Voltmeters go in parallel, ammeters go in series.
Was that any help ?
Skeptic's 4 to 20 milliamp scheme is in very wide use for the reasons he mentioned.