[1] http://money.cnn.com/2015/12/10/news/companies/gm-recall-ign...
I can’t say anything about GM‘s rep in the US, but here in Europe they are not doing so well. Chevrolet was killed in 2015, and Vauxhall/Opel are doing only ok-ish. Chevy had SO many recalls in the years before they killed it.
Uber already has a terrible reputation with everyone in the tech industry for the sexism, bullying, law breaking, and IP theft. Do they really want to be the self-driving car company with a reputation for killing people?
It doesn't take a lot for people to think "Maybe I'll take a lyft" or "Maybe I'll ban uber from London because of their safety record"[0].
They aren't going to kill the market for this - the other players not only have big incentives to make sure they look safe, but you've got a really unique problem when your biggest competitor is a company that controls access to news and which adverts your customers will see.
[0] https://www.theguardian.com/politics/2017/oct/01/sadiq-khan-...