it seems that if you disconnect the battery while engine is running, the engine will instantly die. That's not the case on all of my cars owned other than ferraris. What is the battery providing power to while not provided by alternator that's so critical?
Disconnecting the battery while the engine is running would likely cause the voltage in the system to float which would wreak havock on the electrical gadgets in the car. The ECU would likely go insane and that would kill the engine. I'd add that the potential for damage due to excessive and fluctuating currents are not trivial. I suggest not doing that.
The battery acts as a large capacitor, smoothing out the power coming out of the regulator that converts the AC voltage from the alternator into DC that the car runs on. Without this, the DC voltage would have LOTS of peaks and troughs and would most likely damage the electronics in the car. I'm surprised you haven't had issues trying this in other cars you've owned. Certainly not something I'd try in any car, regardless of how cheap or basic it might be.
Ah, the negative terminal. I thought it might have had something to do with the sense wire circuit going from the battery positive pole to the alternator. If this is disconnected, the voltage goes high and may affect some ECUs (including the engine ones). Whether the alternator sense circuit is affected in the same way by removing the negative pole, I'm not sure.
If you disconnect either end of a two terminal device (a battery), the other node floats and it is no longer in the circuit. So there would still be voltage regulation issues.
This used to be a diag step on old non ecu type cars to test the op of the alt when a voltmeter was not avail Agree — big no no on fragile f car.
