You quoted before my edit about solo travelers. It's a bit more understandable there; you're just trading convenience.
In the grand scheme, though, you are incredibly unlikely to be the victim of a crime in an Uber or Lyft. Sure, it can happen, but it's a bit like being afraid of the potential side effects of a vaccine instead of whatever the vaccine is protecting you from.
And I say that as someone who thinks Uber and Lyft are ridiculous companies with numerous problems and no path to profitability.