Absolutely. But I'm not going to focus on being over the speed limit by one MPH, I'm going to focus on the car crossing the line into me, I'm going to focus on the cyclist on the shoulder, I'm going to focus on the pedestrian entering the road. If I'm five over? Sure, I hit the brakes.
Yes, all of that sounds like safe operation of a vehicle!
Of course, many people speeding are not simply driving 1 mph over, which is why I pushed back on your contention that it's hard to do "other things" while avoiding speeding. And those "other things" are often dangerous and distracting.
Point being, micromanagement of ONE aspect of driving a vehicle (bicycles included) is short-sighted and asking for an accident. There are a number of factors that must be managed in driving, and being over the speed limit by a single MPH is foolish to focus on.