Speeding is defined relative to an arbitrary value
Nope. There is nothing arbitrary about the value chosen. Because you don't understand the background trade-offs, or how the limits are set related to road safety, both in pre-engineered systems which define speed limits based on types of roads, and that weird system that the USA did employ for a while where the limit is set based on a percentile of the average road speed doesn't make it arbitrary.
And why have a limit in the first place? Well even when you set it based on crowd sourcing the average acceptable speed (bad way to do it since there's ample literature showing people overestimate their capabilities), you still have enhanced safety by reducing speed variance - i.e. getting the people going above average speed to stick to a limit.
Claiming that speed limits do not improve public safety is just stupid. Not ignorant, just stupid. You don't even need to research this to conceptually understand why your statement is wrong.