> no more than one collision in multiple years of driving
That's really high, that's worse than what people do (on average a person will probably have an accident every 18 years, none fatal).
And that's with a person watching? That's really bad.
> once every few months is perfectly acceptable
Not really. The people inside it will have no practice (or even ability) at driving. Such a car is not really useful, you'll just make things more dangerous, not less.
The bar for self driving cars is so incredibly high, I doubt you'll see them on regular (non-instrumented, restricted) city streets until we have true AI.
Most likely there will be train-like intercity roads, dedicated (and instrumented) for self driving cars and trucks.
But unrestricted city driving? Very unlikely to ever happen.
Despite how high the accident rate is, people are actually really really good at driving. And computers are really really bad at being reliable.
When you can have a complex computer program that simply manages to have 99.9999% uptime, then we can start to talk about self driving cars. We don't even have that, self driving cars are an impossible dream.
And that 99.9999% number is not just random, it's how good you have to be to beat a human at driving.