It's not about what people believe, but what they are willing to publicly push back against. If such a law was proposed today, I bet it would pass because the only discussions around it would be whether the data can be kept safe and what punishments to dole out if the car owner access this data. Arguments about privacy will be waved away or dismissed without debate.
In fact, let's make a pointless bet: I bet my imaginary internet reputation that the US or EU will pass a law within the next 10 years that requires the continuous recording and collection of data that not only includes GPS, but also face and audio data whenever a car is in motion. This law will impose severe punishments on any owner that accesses this data or deletes it.
I desperately fear for my family and want things to improve, but we are going to lose this battle.
My logical assumption is that all terrorists and pedophiles will concentrate in the areas where they have legal exceptions from being monitored by multiple different parties at any given time. Legislators and the like. To play one of their cards, why would people who love to say "innocent people have nothing to hide" have something to hide?