If you look at it from pc plods point of view snowball, engine off is so much simpler.
OK wagolynn, let's play Devil's Advocate.
Driver stops in safe situation to make an emergency call on his mobile phone (let's say a passenger suddenly takes ill), and the driver puts his car in neutral with the handbrake on, then gets out and stands near to car but leaves his engine running.
Now, what is simple for PC Plod?
(1) Driver has left engine running, but is not in the car.
(2) Engine running when driver has exited vehicle. (Law says you should not).
(3) There are many reasons for being out of a vehicle and the engine still running; for example when there is a worrying sound that demands an explanation.
If PC Plod decides he wants to clobber the driver, he can't choose (1) and (2) is doubtful because of (3).
The answer is that he would most likely pass by without stopping. So, if a driver is sitting in a safe, stationary vehicle whilst using a mobile phone, would he stop to check if the engine was still running? But, if he did, and the engine was still very warm, would he then have to assess whether it had been turned off later; say, just as he arrived?
Much simpler to delete the "engine running" aspect, and save stress on PC Plod's brain.:D