I use the word "cheap" a lot to refer to the dreck found on Alibaba, Amazon Marketplace etc. I'm surprised to hear it associated with GE, one of the finest names in the industry. But yeah, that $7 shutoff is pretty cheap, with its plastic-bodied pull tab for a shutoff. Clearly not meant for daily use. Nonetheless, you don't have to wildly derate GE stuff like you do for cheap Cheese junk - if it says 60A it should be good for 60A (48A continuous). You can run GE equipment on the brass.*
I would shut off power at the main panel, then pull that pull-tab. If it is warped, or comes apart in your hand, then -- well, do this sometime you can afford to be without the charger for a day or two!
One thing the industry has learned through experience is that lug connections are sensitive to torque setting. Recent Code changes now require everyone to use even torque screwdrivers for the little stuff. And a lot of elecricians resent this... somehow a mechanic's beam foot-pound torque wrench is $30, but a screwdriver sized inch-pound torque wrench is $85. So some electricians (and most handymen/homeowners) just don't use torque wrenches.
Given the amount of plastic in this thing, it wouldn't surprise me if the heat was coming from a loose connection at a lug, it's making a fairly considerable amount of heat, and that is traveling up the bus bars to scorch the plastic. Thank God it's a metallic box!
It might be fixable by opening up the box, cleaning up wire ends and retorquing, and likely the torque required will be just within the working range of a mechanic's torque wrench, so ask your neighbors. However if the box is damaged, this will be your opportunity to get the better box.
Just don't confuse "more features" with "better". You don't need a circuit breaker at that location. I would say a higher ampacity would be "better".
* "On the brass" is an old 1900 era streetcar term for "to the floor". Meaning you have pushed the power controller onto the brass stop. Fair chance if you find a power controller in a museum, it'll have the familiar GE logo.