that is exactly what the government does with the CAFE standards.
No, it isn't. The CAFE standards traditionally used the weighted harmonic mean of the mpg values, which gives exactly the same result as the weighted arithmetic mean of the economy expressed in gallons per mile. There are some other quirks- dual fuel vehicles are treated much more favorably than they probably ought to be, for instance- and the standards were recently changed to give bigger vehicles a break. But the larger point is that the EPA isn't completely stupid and does realize that the arithmetic mean is not the correct way of calculating average fuel economy.