1. Transportation and distribution losses are not unique to electricity. If you consider the amount of energy expended to get the energy from the ground and into your tank the distribution losses are greater for oil than they are for electricity.
2. Batteries will probably never achieve the energy density of liquid fuels, however, the most efficient gasoline engines still only transmit 25-30 percent of their energy to the wheels, whereas electric motors transmit around 90% of the energy to the wheels. So, batteries don’t have to achieve the same energy density to get the same number of miles on a charge as a ICE would on a tank. (Admittedly, they will have to improve to at least 400W/Kg. with a 50% reduction in cost) to make a 300 mile electric car practical for most Americans.) However, when that happens, and it will, the per mile cost of fuel 3 cents vs. 12 cents and the greatly reduced maintenance cost will make the electric car competitive for most applications.
It's not important what the number on the battery says. The test is simple, it's called "distance traveled." If you can come up with a battery that can move the car for 300-400 miles at 50-60 mph then this battery will be a reasonable option.
But the charging time of that battery is still a factor. We know that it doesn't take much time to fill the tank in a car. Perhaps 5 minutes if the tank is large. Fast charging of a battery is theoretically possible today, with damage to the battery; but will that new battery be capable of fast charging? Currents there will be huge.
The problem here is that when you fill the tank you are pouring a chemical that is ready to burn. Batteries take something else and make that chemical while you are waiting. That chemical reaction is much slower, and it is not entirely repeatable; as result, a battery has a limited number of cycles. A gas tank has no such limit.
The electric motor is great, by the way. I don't think many people complain about that part. The problem is only with the battery - it is large, heavy, expensive, fragile, takes forever to charge, and it wears out. If someone finds a way to store (or to produce) electric energy with a battery that costs about the same as an empty gas tank then we will see mass migration to EVs. Until then - sorry, the Leaf is not a good car for a mobile person. It is an OK car for a cube farm guy who only goes to work and from work, 10 miles per day. (But if someone drives that little then it makes no sense to spend $38K on a car.)
So, batteries don’t have to achieve the same energy density to get the same number of miles on a charge as a ICE would on a tank.
Lots of people live in climate with winter. This "lost energy" is not exactly lost to them. Sometimes it's barely enough to heat the cabin, even when you insulate the radiator. An electric car would go maybe 5 miles in winter, even if that much. You can't use a car without heated windows - you need to see where you are going.
when that happens, and it will, the per mile cost of fuel 3 cents vs. 12 cents and the greatly reduced maintenance cost will make the electric car competitive
It all depends on cost of energy sources. Electric power is largely produced with materials of Earth's crust. All other methods (wind, solar, etc.) are very expensive and very inefficient. If EVs are adopted en masse then the cost of electric energy can easily go up - not just because utilities are inherently evil, but simply because there won't be enough electrons to run around. How many power plants, nuclear or otherwise, have been recently constructed? Efficient methods of mining coal are being shunned for aesthetical reasons; mining coal underground is an extremely dangerous manual labor. Domestic oil is neither mined nor purchased from Canada. You can't transport electricity across the ocean; so where will those joules be coming from?
Re efficiency, you are ignoring total system efficiency. If you have a Rankine or Brayton cycle generating your electricity, you are in the range of 33% to 65% HHV. You are counting the heat engine efficiency of the ICE under the hood, but ignoring the heat engine efficiency at the end of the power line.
Battery R&D has stalled over the past 30 years and I don’t think you’ll ever see the improvements needed to make them competitive. Besides, better batteries and motors require rare earth minerals, 97% of which are in China. It seems the earth’s crust doesn’t that much of the essential rare earths.
The overall toxic waste problem is hugely against batteries, too. Not only do you have up-front toxic messes to extract and refine rare earths, but you have the downstream disposal problem as well. With gaseous or liquid fuels, you also have up-front messes, but they aren’t as toxic as with rare earths. You have waste streams as the fuels are burned in ICEs, but those emissions are very clean now and are temporally and geographically disbursed. What in the world is going to happen to the mountains of used batteries if EVs take off? How will these be recycled?