Durability, dependability, when your life literally depends upon the outcome of the first shot, you want 100% confidence.
Variable scopes have only recently been on par with fixed scopes when comparing image quality and repeatability.
A sniper is almost never going to engage a target closer than 100 yards, so he would not need to lower the magnification to 4 or 6. At 100 yards, you can easily engage using 20x or more if using a fixed scope.
Edit to add:
Apparently some misinterpreted my last sentence as to mean that the snipers were issued 20X, it did not mean that. It was to point out that variables are not necessary. They were over hyped as necessary by the scope manufacturers to sell more. A fixed 10x or 16x or 20x is all one needs to engage a man sized target from 100 yards to over a 1000 yards in the role of a sniper.
Fixed scopes have always been more dependable. Even today there is a risk of the reticle walking when changing magnification.