Let's all hope your assumption is correct and we won't ever need to find
out.

Back when my engine used to run :-(,
the warning buzzer for low oil pressure (and overheat) would come on as soon as
the key was turned. It would remain on for a second after the start button was
activated until the oil pressure climbed to about 40 pounds (enroute to 60-70)
and then shut off. I think this is a better system, only because it
demonstrates that it is working every time the engine starts.

Who waits 30-45 seconds after turning the key part way to crank an engine?
Probably nobody. The entire system could be gunny sack and you wouldn't know
it.