Burnt connectors were already a thing on far less powerful cards, albeit not anywhere as common as what may be on its way here. The problem here is that if you have bad contact on one wire, the current will get pulled on the remaining wires, those will get warmer, one of them may have a worse connection than the other, then its share of current will be carried by the four remaining wires, which will get even hotter until yet another connection fails, then you have the load going through only three good connections that are getting even hotter, rinse and repeat until catastrophic failure.
The only way to avoid this would be for GPUs to either do per-wire current monitoring/balancing or splitting the VRM phases evenly between pins so the VRM can detect when phases aren't getting the expected amount of power from the PSU, reduce the affected phases' current limit to a safe level and tell drivers to notify the user.