> cooling

At the very most this will be < 5% performance increase because they'll need to match the best of BLDC (~90%) and 100% is simply impossible as there are losses that cannot be engineered out (thanks Physics). Also that 80% -> 90% isn't all heat, I imagine the amount of cooling required to stay roughly the same.

> batteries may be more efficient when you draw less power

> from them, etc.

From memory, a switch mode power supply is one of the most efficient at about 90% - but you really have to design it well to get that kind of efficiency [1]. The batteries were a soft point for cars. But there's quite a bit of efficiency to get from phase control algorithms which would be in the motor control circuit.

[1] https://en.wikipedia.org/wiki/Switched-mode_power_supply