> by making it light
If there's one thing that EVs are not, is "light". Model S ranges from 4,561 to 4,941 lbs. A model 3, 3,648 to 4,250 lbs. A Nissan Leaf - 3,538 to 3,946 lbs.
In comparison, a Honda Civic weights 2,771 to 3,012 lbs.
Regenerative breaking is nice but it's very dependent on the particular drive and terrain. Heaters are power hungry as there is very little waste heat that can be used (again, due to the high efficiency), unless they are heat pumps.
The main reason they can go so far with so little energy is the efficiency of electric motors.
> as hydrogen has similar power/weight characteristics to gas
No it doesn't! It has horrible energy density per volume, compared to any gas or liquid fuels. You can improve this by using high pressures (energy loss) or cryogenics (even more energy loss). But it's pretty bad to begin with. Turns out that the best way to store hydrogen is by adding some carbon atoms to it.