Mass counts much. It's not just about accelerating a still object (car) out of friction. But it's also about working against gravity (g). If the car's acceleration vector is at some angle with gravity (ie, when not perpendicular), more energy will be required to accelerate (when climbing slops), and to break (down the slope).
This is very much clear for aircrafts, and other flying objects.
Edit: Inertia is also a reason for energy loss in cars (and other moving objects), which increases with mass.
Rolling friction loss is related to speed and is occurring constantly as you drive. That energy is just gone immediately, unlike inertia, which is stored. Say you spend 50% of your time accelerating and braking, and 50% keeping speed. If you regen 80% of the energy and accelerate with 2.5x the power you use to cruise, you're using twice as much energy on friction as accelerating.
I don't know how good exactly electric cars are here, but considering that a Tesla can work as a taxi in the city, it must be pretty good.
[edit: punctuation]
Unless these batteries can accept charge faster, their extra mass won't be offset by more regen.
The same reason city driving is less efficient?
That's just the voltage across the terminals. The reason why this works is precisely because current doesn't go from 0-100% with the voltage. PWM is relying on the inductance of the motor to keep the current the same as it would be if the average voltage was applied across the terminals.
It's actually friction, for electric cars. Regen is pretty effective at recapturing acceleration, so the energy lost in the wheels is the biggest factor.