If the voltage doesn't kill you, does the current capability matter?
You assume that voltage and current are independant, they are not.

It is indeed the current which kills (can stop your heart for example) but the voltage is needed to make that current flow in the first place.

Conventional "wisdom" says that working in a main panel calls for more caution because one might make contact with 400A service, as compared to the 20A one is facing working at the end of a typical circuit.
That has probably more to do with the dangerous consequences of a short circuit than the danger to a human. The 20 A sise is fused so a short circuit will blow the fuse. At the 400 A side there will be no fuse or one with a much higher rating so more current has to flow until that one blows.

it doesn't matter how much current is on the supply: The body will only carry the milliamp or so admitted by its resistance.
That is correct.

Indeed a mains of 20 A or 200 A, there is no difference regarding you feeling a shock as the current only needs to be a few mA. Both can deliver that current.