Apparently EVs do have coolant, ethylene glycol, to dissipate battery heat and use that for heating. On especially cold days they use a supplemental heating element, that as NoVaGT points out, drastically reduces range. AC uses an electric motor to circulate refrigerant.
As pointed above, that's wrong. My Tesla has a coolant reservoir, just like the Bullitt. The battery pack and motors need cooling too, but obviously not as much as an ICE powertrain. My 2021 Tesla has a new heat pump system, which relies more on coolant than previous models.
Because electric heater elements require beefing up the alternator system since electric heating is extremely current intensive. Using engine heat is far more efficient and easier. In some situations it's preferable to do electric though. And not even just on EV's. My friend's Audi Q5 TDI has an electric cabin heater since diesel takes too long to warm up in cold climates.
The Fiesta's and Escapes of last-gen can have an electric booster heater as well as a normal heater core that will heat up the cabin when it's below 40*F or so, so it is possible. As for OP, since it's a dedicated track car, may as well pull the dash and remove the HVAC case (and compressor, etc.) if you don't care about any sort of air blowing at your face/other regions. Otherwise I'd say leave it as it is if you don't plan on removing anything - why plug the heater when you're not removing it?