American aviation legislation is a model of simplicity in comparison.
I don't believe that's the case. You cite a single example, the low flying rule. But there are plenty of cases where US rules make specific demands, while UK ones leave it to the aircraft commander to make a sensible risk management decision on private flights:
Examples:
Use of oxygen
Fuel requirements
Requirement for alternates
Alcohol consumption (at least until recently)
One could argue that the airspace structure was an example too.
Unfortunately, it seems that ICAO is encouraging the CAA to go down the road of detailed legislation in even some of these areas. It is sad that in an age where general Health & Safety regulation seems to be moving away from the prescriptive towards a rather more enlightened approach of "think about it, manage it, document it", we seem to be hemming our pilots in by more detailed regulation. It may well have a detrimental effect on safety.