I would counter that the exact opposite will be the case. I think insurance companies are exactly the people who will force it to happen once a body of evidence is gathered to show the safety advantages of autonomous aircraft
Until they have a fatality killing 500 people that a human could have recovered.
The other issue there is actually proving your case to be correct. The amount of autonomous flight data you would need is huge given the number of human powered flights that exist now. Flying a testbed around the world a few times is not the same as the millions of hours that humans put up every year.
And for the insurance companies they have to consider the original title of this thread can computers deal with the weird failures that occur in aviation