Ammeter heating up.........

Ammeters were common when generators were used, before alternators. Generators tend to have more voltage variation on output, so I suppose those systems were less amenable to using voltmeters.

Voltmeters will not tell you if the battery is taking a charge or supplying current to the system so voltmeters have that weakness. But, ammeters tend to be harder to interpret; charging AND discharging ammeter indications are actually normal readings for a good system with an ammeter. So they are harder for most people to understand; 'user friendliness' is a big disadvantage for ammeters.

The ammeters in the Mopars were cheap and not durable (as the OP found), but ammeters used in small general aviation aircraft, like Pipers and Cessnas, are perfectly good after 40-50 years. There are no with in-air fires, other failures, and no Airworthiness Directives have been issued, so there is no compelling reason to replace them; they are rock solid reliable. So in general ammeters are not a problem per se, just the cheap ones in our Mopars.

FWIW, I am keeping the ammeter in my '62 Dart which is 98% original. But I put voltmeters in my rally cars. These seem to be the best choices for me for the given situations.

Burned up bulkhead connectors can/will occur with or without an ammeter or voltmeter; it is mostly a matter of where you route the heavy currents (like charging current to the battery), and how well the connections are maintained.