USB Charge current indicator ?

I have several of those. They work well. Check other sources for dramatically cheaper prices.

many USB cables are capable of delivery of a decent charge....

When you have a lab powersupply that can be set to 5V and which also has adjustable current limiting, would you always set the current limit to

5A when experimenting or would you turn it down to .5A and only increase it in cases where more current is required?

I would. So does USB.

usually not, while you are not supposed to draw more than 100mA until enumerated and allowed to do so but many thing don't care as long you don't short the supply

That only works if your lab powersupply can negotiate with the load either by resistor values on D+ D- or data exchange.

DO NOT ASSUME THAT THE DECISIONS MADE BY THE VENDORS OF THE POWER SUPPLY OR THE DEVICE BEING CHARGED ARE RATIONAL AND CONSISTENT.

About the best you can hope for is for the device to manage the current and set the power supply current at a level high enough for that to happen and low enough so it doesn't catch fire if something goes wrong.

In the example of the lab powersupply I am not talking about USB but just about a lab powersupply to do some electronic experiment on the bench.

E.g. I have a separate "station powersupply" that provides 13.8V at 30A. Of course I use that only for tested equipment and not to power some experimental ciruit with alligator clips. I use the separate variable lab powesupply that has variable voltage and current limiting, set to some current that is not far above the expected current draw of the circuit.