I've had Geico since 1977, when I first started working for Fed Govt. As someone else said, back then you had to be either military or fed employee, not the case since Warren Buffet bought the company.
In that time, I have had 4 accidents someone else's fault, 1 that was my fault, 1 theft of radio and associated damage, and 1 stupid accident backing into a tree.
Oh, and they sent a flatbed to pick up the Porsche when it died by the side of the road the first month I got it.
They were always easy to deal with, use a decent bodyshop here in Augusta, and the rates are neither highest or lowest. They have never said anything about the radar detector and neither have I.