> My problem with generic chargers is a bit less subtle: my phone battery melted.

Which is a problem with the electronics in your phone not the charger. All Lithium-Ion batteries need to have an on board charge management IC to guard against overcharging. The power supply is just a dumb DC supply possibly with a way to request higher currents. In the end it is the responsibility of the phone electronics to limit current into the battery. Either they failed, were poorly designed, or the battery itself failed.

Unless the cheap transformer in the supply failed, and the charger started pumping wall current into the charger. Here's one disassembly of a crappy charger https://www.youtube.com/watch?v=afePhiXpsoA