[oil pan 4]

It's not possible for batteries to exceed the stored energy of a gas tank. Each gallon of gasoline weighs about 6lb. Each gallon is something like 33kwh.
The battery will always have to contain the fuel and the oxidizer, have something to conduct the electricity away from the cell, have structures to contain, separate and support the anode and cathode. Realistically scientists could probably double the energy density of batteries. Rumors or "breakthroughs" that claim to increase the energy density 4, 5 or 10 times the current energy density are BS.
The secret to gasoline, diesel is all the air you need to activate the reaction is all around us.
Low effort efficiency for gasoline is around 25%. For energy density and refuel vs recharge time liquid fuel always wins.

I have seen a car get over 200mpg. A friend towed there toyota car. The cars manual warns against flat towing with the engine off. So they leave the car in neutral with the engine on so the transmission can continue circulating it's transmission oil. It got about 220mpg being towed at 60 to 65mph.
Even the near perfect efficiency of the leaf it only gets the equivalent of 140mpg. Let's say I used gasoline to power a magic fuel cell to charge my leaf, I'd probably get 50 to 70mpg doing that.
Running a car off a "lawn mower carburetor" appears to barely beat electronic fuel injection in an 4cyl car and appears to improve fuel economy of a V8. 50 years ago getting nearly 40mpg in a small v8 would be crazy mpg. Now it's meh mpg that's using 5 and 6 speed transmissions that didn't exist 50 years ago. So the crazy high mpg numbers from antiquity are not reproducible even with modern tech like electronic fuel and spark control, electronic oxygen sensors to "tune lawn mower carb tests", transmissions with 6 or more forward speeds, amazingly efficient tires and much improved aerodynamics.
Putting a "lawn mower engine" in a car appears to only get around 20 to 30mpg.
There's no free ride.

I was able to double the fuel economy of my 7.4L suburban that has 3 speed auto and 4.10 gears, getting equal to or better fuel milage than new suburbans. But nothing I would consider crazy high numbers. Just by turning the carb for lean burn while rolling down the road.