Most people compare a chauffeur to an Uber by checking the app once, on a quiet Tuesday afternoon, and deciding rideshare wins. That's a fair comparison if you only ever fly on quiet Tuesday afternoons. Almost nobody does.
The real comparison isn't fixed fare vs rideshare. It's fixed fare vs rideshare on the specific day you're actually flying — Friday evening, a delayed red-eye, the Sunday after a long weekend, AFL finals week. That's when the numbers move, and that's the comparison nobody seems to publish with actual figures attached.