This would stop the currently exponential pace of growth from outpacing what society, and regulation, can adapt to. Thus avoiding the inevitable crash that will happen when we lose control of the exponentially accelerating train of technology, and it flies off the rails.
One could argue many such governors are already in place.
Some are financial, others are societal, a bunch are based on actual proactive intervention (e.g. through international laws because of ethics considerations).
The more important question is: who governs the governors?
I suggest we get some Frankensteins, and have Lenny “The Guvnor” McLean.
If we define ‘governor’ as a system whose task it is to regulate sth to keep it at a constant level, a good successful existing example would be central banks. They regulate money supply in order to keep inflation at a constant, prescribed, level.
But that would be more like the steering mechanism employed before the invention of the governor for steam engines: actual persons trying to regulate the speed of the engine by manually pulling levers.
The equivalent to the governor would be an automatic intrinsic feedback loop that, once established, is continuously and automatically working without manual intervention.
So your steam engine governor analogy might be not quite fitting.