If your battery has just 'lost its edge', causing S/S not to activate, the voltage monitor probably won't reveal much, as AndyRKett says. In my case the (then) new car's battery was still rated good enough for S/S to stop the engine, but the the voltage dropped rapidly; from an indicated 14.2V down to 11.6V in less than ten seconds, even without lights or AC on, at which point the S/S quickly stepped in and restarted it. In that case the monitor came into its own and showed the problem.
I'm not sure about later 500's but if I turn my engine off with the key both the headlights and brake lights also turn off, not desirable in traffic. It also means other systems have to reboot and reconnect, such as satnav, Bluetooth and dashcams, and if the stop is brief they can get confused if they haven't had time to shut down completely. In any case with FIAT's system you're still using the same starter motor and battery whether it's done by S/S or manually.
Is there a minimum time one can allow a car to idle under the legislation you mention?
My S/S EFB battery is now six years old and the S/S still works properly but conditions here are a bit kinder to batteries.