This is a male perspective.

My wife will not ride alone in Uber's because she's had one too many uncomfortable -> possibly dangerous situations.

This appears to be true for all of her friends as well.

And this is hilarious anecdata. I also know lots of women who use Uber all the time and have no issue with it.

It sounds like your wife is overly sensitive and I honestly don't believe you know the attitudes of all of your wife's friends with regards to Uber. This is classic "make up some rubbish to prove my point online."