People do NOT like lock-in by vendors. The situation with Keurig is akin to purchasing a pair of Nike sneakers, only to find that you can ONLY use Nike-branded laces or inserts!
One other advantage of this system is that you could be sure of the range of your vehicle. As batteries age their ability to hold charge tends to decrease and in this case the system could cycle out older batteries so any battery you have on your trip will give like new performance. I think your analogy of the battery is like gasoline is a good one. You really only borrow or rent gasoline one tank fill at a time. Here, the stored energy in the battery is the gasoline or fuel. How do you feel about recycling the batteries in a battery powered device even if they're rechargeables? Or the tires on a car that wear out? I expect you don't have a very strong affinity for them.
You'll not doubt pay more for this service than if you just paid for the electricity at home but if you charged on the road you'll not only pay for the electricity but also something for the cost of building the charging station and its maintenance. Another advantage could be that you might want to exchange batteries when at home so as to prevent a big surprise when your original battery won't hold charge any more and you would have a several thousand dollar expense getting a new one. Likely this cost will be spread out over the life of the car rather than in one big gulp.
You gotta' take into account the Second Law of Thermodynamics. In a cyclic process entropy is created when work is performed like moving the pistons in an internal combustion engine to get the vehicle down the road so some of the energy content in the fuel will not be converted into motion. One consequence of this is the fact that vehicles have radiators to dissipate the heat that cannot be turned into motion. Even electric motors, which are very efficient, get warm. The power plant that produces electricity can't convert all the heat used to run turbines into electricity. Similar arguments can be made for wind powered turbines, though the wind is kind of "free" energy when it blows. The electric current used to charge batteries generates heat in the batteries. And discharging batteries to run electric motors in cars get warm. So, yes, the 1st law can be used to calculate the energy required to convert the combustion products back into fuel but more energy will be put into fuel manufacture than was converted into the work of motion. My guess is the total efficiency of the cycle (wind electricity, convert CO2 + H20 to fuel, burn fuel in vehicle, move vehicle) is somewhere near 15% or less.
According to a post above using wind generated electricity to make the conversion would require 40 acres for 200 liters of fuel. To give an estimate of scale: the USA consumes about 3.2 trillion liters of crude oil per day, so to make this fuel as a replacement using wind power would require 636 million acres. Not all the crude goes into fuel so the numbers may be off some. The land area of the continental US is about 1.9 billion acres, so somewhat less than 33% of the area of the US would be required to replace crude oil based hydrocarbon fuels. Considering wind doesn't blow well everywhere, a lot of land is used for agriculture, forests, national parks, deserts, etc., a significant contribution to a wind generated fuel source doesn't sound likely here. Nuclear fission or fusion generated electricity might do the trick considering the likely land area requirements for those plants. There are well known problems with nuclear fission electric production and nuclear fusion produced electricity hasn't been made commercially viable yet.
Are folks who write about phoney cures legally liable for the deaths that could be prevented by scientifically proven methods? I'm not sure it's been tested in the courts.