Why not start by charging normal rates -- then raise rates according to the driver's record?
Short answer: Because that would cost them $$$ in profits, as golfer0012 was saying.
The insurance companies try to predict how much money they'll have to pay out in claims per driver. They look at how much money, on average, driver "X" will cost them based on crash history, age, etc., and compare them to the statistical average, then they set the rate. In short, it's pre-emptively stocking up the cash in anticipation of a claim. I agree that it is unfair to responsible young drivers. Unfortunately, there are also enough irresponsible young drivers on the road.
Some insurance companies do a more in-depth analysis, which is why a handful of them will forgive minor traffic infractions like speeding 15 km/h over the limit, if it happens once every couple of years - said driver is not statistically more likely to crash than any other average driver. Others use any variation from "absolute law abiding driver" to raise the rates.