"They need to be better than an experienced human driver"
Ideally, and as an end-case scenario, yes. What I meant was that self-driving cars will be *immediately useful* when they are as good as an average driver because that is the point where introducing them would not be a change for the worse. And from that point onwards they will only get better, since by collecting and pooling their experience they can build on billions rather than millions of miles driven.
"Why should such a driver hand over to the equivalent of a less experienced version of himself"
He shouldn't... but the problem there is that 90%* of drivers think they are better than average, and most will be quite convinced of being better than the self-driving car even if they are not. The key point in the end will be convenience: Even if I think I am a better driver, do I think the AI is at least good enough that I can trust it to drive? If yes, most people would rather spend a couple of hours of productivity, entertainment or rest and allow the car to drive rather than drive themselves. (In fact seeing what is already happening eg the Tesla fatal crash, some people are already far overestimating the AI capabilities)
*Rule-of-thumb guesstimate, but I'm pretty sure its not far off the mark.