The bases offer vehicles to get people going, if they want to travel and look around before they buy. There a thousands of cars for sale privately within a short drive of the base.
Again, you are just making the most favorable assumptions and I'm sure that while you can probably buy cars on the base you can't presume everyone will find what they need.
The fact is the bigger problem comes when you have to sell in a hurry because you are leaving. Which is why if you have your own car from the states you just ship it back (which the AF again does for you) but no one wants a right hand car in the US, so that's a non-starter.
Finally there is the financing cost hit you take.
Again, since I looked up the Passat I'll use that.
In the US you can buy the car for $20,000 with $2,000 Sales tax. Let's pay the sales tax with cash and put 20% down and finance the rest for 5 years at 6% interest.
That's a monthly payment of $340 per month.
After one year you get shipped off to the UK, and so you sell the car.
Well the first year the car depreciates about 20%, and so what you owe on the car and the loan amount are both about $16,000, so now you have no car but you get no money from the sale, but you are square with the bank.
Of course besides the first year car payments you are also out about $6,000 for your down payment and sales tax.
So now we go to buy the car in the UK.
Well the same car in the UK goes for $38,000 but we want one that is a year old and its also depreciated by 20% and so you find one just like the one you sold back in the US for 20% less or $30,400.
So now you come up with $6,000 as a down payment and finance the rest for 4 years at the same rate of 6% (this makes this loan end on the same date as the original loan to make the accounting simpler)
Well that new payment is $570 per month or $2,800 per year more then you were paying for the exact same car in the US.
Now the four years are up and they are shipping you back to the US and you sell the car for its nominal value (15% per year depreciation after that first year) or $16,000.
So now you go to buy the same car you sold in the UK, and since it's now worth $8,500, plus $500 in sales tax, or $9,000 to get your exact same car you sold in the UK back.
Leaving you with $7,000.
BUT
You paid $6,000 in a down payment that you wouldn't have had to pay in the states, and you also paid an extra $11,000 in finance charges over the 4 years.
So
At the end you are $10,000 in the hole by buying the exact same car in the UK that you had in the States.
Change the price of the car a bit, the length of time you own it in the states vs the UK, and the numbers shift a bit, but the basic math stays the same, it saves you to let the AF ship your US car to the UK.
If you're smart, you should probably pick a model of US car that Brits are willing to pay a lot for and sell it when you leave (I'm sure there are some).
Arthur