Currently 33,000 people die each year on American roads. Let's say that self-driving cars cut that number to 10,000, but that almost all that 10,000 is because of failures in the self-driving car technology. Will the American public accept that? They've behaved irrationally before, they could again.
I don't accept the premise that the choice is irrational. Given the existence of a skill set that helps avoid accidents, it is quite rational for individuals who possess that skill set to choose their own judgement over a random chance of technical failure.
Also, I don't accept the premise that surrendering agency in exchange for safety is, in the context of human emotional needs and the long-term evolution of society, a rational choice.
I didn't say all accidents were avoidable, but many are. As you state in the part of the post I responded to, there will also be accidents with driverless cars. They also will be unavoidable. I think the desire to retain as much control as possible over one's fate is one of the better parts of human nature, not an irrationality. Bear in mind, no data exists demonstrating the real-world danger, or lack of it, in such a system.
You would rather increase your risk of dying than give up driving?
Absolutely. The same applies to hiking in the mountains with bears and cougars, drinking, eating meat, swimming in the ocean, being out in Georgia Strait in a small boat a south-easter, doing street photography on Hastings, etc.
I would rather see the costs of this stuff put into demanding driver ed and testing. The half or so of the populace that would be summarily booted from the ranks of drivers would create the critical mass necessary for efficient public transit. Win-win.