ATC cannot authorise it in Class G, though. As already mentioned, it's for "See and Avoid" reasons.
Some years ago I endured a "discussion" on here with a certain pilot member of the forum (from USA, I believe) who obviously didn't agree and was trying to castigate pilots flying quite legally in Class G just below the base of Class D controlled airspace around London "in case he decided to come barrelling out" (iirc, his choice of words) of said airspace in his heavily laden 747 at high speed.
I asked him if his operator had written dispensation from the CAA to exceed 250 kts in UK Class G airspace and he went potty - he obviously hadn't.