While it may be a difficult concept to measure and my experience is purely anecdotal and specific to me, the presumed liability in the Netherlands had a huge impact on my driving when I moved there.
I was driving for a decade there before I threw my leg over a bike and got to experience it from other side.
For me, it's a no brainer for improving bike safety and the perception of bike safety.
I understand fully the abhorrance at the thought of being responsible for an idiot, but NL do things differently too;
When I started commuting I would meet a "light" control within a couple of weeks of the winter clock change. On the spot fine for each missing light. (Weekend night were popular for random controls for lights too).
The use of a phone while riding is now subject to a hefty fine.
Mopeds (brommers) are frequently pulled for violations.
Try riding on the road when a (compulsory) bike path is available - no bike priority then!!
In other words, it's not a free for all for cyclists.
Also, schools teach cycling etiquette and many schools do field trips on bikes so responsible cycling is ingrained from a young age, while compulsory driving lessons train drivers how to deal with bikes.
I don't have access links to them now, but there are stories of traffic lights changing patterns in the rain to facilitate bikes (Rotterdam) and regular reviews of traffic flows all designed to minimise the reason for cyclists to break the law.
Finally, there's the infrastructure which is clear and well maintained making it very clear who has right of way and when.
It's not just one thing that makes a difference - it's a whole package. It's complicated and makes it difficult to measure the success or otherwise of one thing. It should be remembered that the situation in NL developed over decades, often in the face of intense hostility from the car/vehicle lobby.
Oh, a priority law does not make any but the most foolish careless or adopt a devil may care attitude. The sheer number of bikes means that you always have to be on your toes.
