...That's why I believe there must be some other reason for the overheated connectors.
Receptacles with weak grip, due to repeated use and repeated overheating. Weak grip can also present an increased electrical resistance, which leads to localized heating. Replace those weak receptacles.
Burnt receptacle or plug contacts due to connecting and disconnecting while under load. Burnt contacts = higher resistance = heating. This is why you should flip the breaker feeding the receptacle OFF before connecting or disconnecting.
Frayed wires inside cordsets where they meet the plug — broken strands due to the extra flexing (work hardening/metal fatigue) that happens when cords are connected and disconnected. Fewer intact strands = higher resistance = heating. Grip the plug, not the cord, when connecting and disconnecting.
These are the most common causes of a cordset overheating when anything near the rated load is applied. It can all be avoided with proper handling (grip the plug not the cord!), use (turn the breaker off!), and maintenance (replace those weak receptacles!).
The plug connection fails because of damage, not because of the load. It would be like trying to tow a 10,000 pound trailer with a 15,000 pound rated hitch that's been cut halfway through, then blaming the trailer when the hitch breaks.