I think we're off target with the gas/brake thing as we are actually discussing Stop Start not continuous motion.
With stopping and restarting you really can't do one without the other.
I don't know how everyone else stops, but I tend to use the brakes at some point in the process.
Sure, a heavy object has more mass, but I gave the problem away with the Force, Mass, Acceleration formula, the bigger the mass, the more force (energy) is needed to accelerate it.
Anything saved due to the extra kinetic energy is more than wasted by the need to accelerate and reaccelerate the larger mass, not just in stop start situations, but all situations.
If it was that simple, we'd all be driving 5 tonne cars that never stop, but we aren't, we're driving lighter and lighter cars with more systems that increase efficiency.
The point made way back was there are more efficient systems of stop start than the system Fiat use on the 500.
I am not knocking Fiat for this, it's a cheap system they haven't had to develop, though I am saying it doesn't work as well as other systems.
Sure the 500 may use a regenerative alternator, but it also uses the engine to power it, so when it comes to a stop it'll restart the engine with the normal battery and will then work the alternator to recharge the battery.
It will not leave the battery under charged until it can recoup that used energy in some way for "free" later and as it can only store energy in one place, it's first instinct is to replace that energy and power the alternator.
Now a system that doesn't use the main battery to perform a restart, but stores this free energy in say a capacitor, doesn't need to work the alternator any harder to recharge the main battery after every restart as the battery hasn't been discharged.
It doesn't leave the main battery under charged has it hasn't used it, but it can leave the capacitor empty until the car recovers this free energy again to charge it up.
One system is using energy from one main store to restart the engine that then needs energy to replace it after the event.
The other is using energy stored separately from the main store, so doesn't need to replace anything into that after the event but collects this energy before the event.
The problem with such a system was always with the fact the energy recovered wasn't quite enough to perform a restart with the normal starter equipment and the energy to power it exceeded what really needed to restart a warm engine.
So manufacturers developed the alternator to do it as it's more efficient, so less power needs to be collected before the event to perform the restart in the first place.