Walking in Switzerland isn't without risk of collision from street cars, buses, cyclists and cars, especially for an unsavvy 5 year old. But the short leash rule extends to areas of parenting beyond just long walks to school. America is obsessed with infantilization all the way to the legal drinking age being fixed at 21 and strictly enforced.
You can thank the Reagan Administration for that one. The Department of Transportation had ideological scruples about mandating airbags, and came up with numbers to indicate that raising the drinking age would decrease automotive fatalities by a comparable rate.
Before that, the drinking age was up to the states.
To be honest I think Federal laws like this that carve out "obey or be punished financially" dictates should be outlawed and unconstitutional. Or if the Federal government wants to make funding conditional then the taxes for that initiative should not be enforceable for the state that chooses to forego that service.