Energy density on mass is not entirely meaningless. A heavier car requires larger tires. That makes the tires a more expensive continuing cost, and creates more particulate pollution. A heavier car also requires larger brakes and pads (though electric cars can offset this with regen). A heavier car also puts more wear onto the roads. A heavier car also makes the car slower at a given horsepower, and have worse handling characteristics.
So metrics like energy per kg, energy per volume, and energy per $ can all be relevant.
In theory yes. In practice, the mach e handles very nicely compared to the mach 1. You'd not buy the latter in favor of the former for it's raw performance as the mach e is simply faster. Brake pads last longer because of regenerative breaking (i.e. you hardly use your brakes at all). Tire wear on a mustang is something to be mindful of. But then doing donuts seems to be a thing with these cars. Ridiculous torque has a price. You see the same pattern with other EVs and increasingly high performance electrical sports cars breaking all sorts of records.
Energy per kg is relevant when weight matters. For example in electrical planes. In cars, $ per mile is the one to focus on. Of course that continues to improve as energy density improves so they are somewhat linked.
So metrics like energy per kg, energy per volume, and energy per $ can all be relevant.