I don't think you're weird, but I can't imagine life without them. I live in the city, and our only parking option is on the street. Whenever there's a parade/festival/event (which, I live in NOLA, so that's a LOT), if we move the car we end up circling for an hour when we get back before finally finding a spot three or four blocks away. And then trying to find parking wherever we're going is equally challenging. So if it's not within walking distance, it's Uber/Lyft or stay home (especially since the streetcar line by us has been closed for years since the Hard Rock Hotel collapse). But even when there's not an event, it's just so much easier to get door to door service. And it solves the problem of drinking and driving or having to have a designated driver.
I've used them all over the country, both with people and alone, at all hours of the day and night, and never felt sketchy or uncomfortable. On the contrary, the drivers have always been friendly and helpful, often going above and beyond the call of duty. If you ever find yourself in need of a ride, don't be scared. Use common sense precautions as detailed above, and then go for it!