Anet A6 ERR MAXTEMP BED error
I'm posting the answer here hoping that will help anyone that encounters a similar issue. A post on another site indicated that these boards are known to be problematic.

After some digging, I came up with the schematics of this part of the mainboard :



I'm not an electronics genius, but clearly it's not the capacitor; so that leaves the pull-up resistor or the microcontroller.

Since the printer is already unusable, no harm in trying to replace the resistor, which is located just next to the connectors; for the bed it was the second from left, but if you encounter the same issue with another input, you may need to locate the proper one.

Make sure you have the proper tools and knowledge for removing and soldering SMD components; in my case it was a 4k7 resistor in 0805 footprint.

Bottomline : replacing a less-than-one-cent resistor saves a month of waiting for the delivery of a $25 board.