Drivers care that lots of people use Uber and you care that lots of drivers use Uber. So there's definitely a network effect. It's just a lot weaker than something like Facebook because I don't care how many Uber drivers there are in Memphis if I'm in Salt Lake City. It's even weaker than that because the geographic area is more like "within 10 minutes of me". You can see a competitor relatively easily getting a toe hold by starting service at a specific time for a specific area. For example, the popular bar street on Friday/Saturday nights.
The problem comes with your "a dollar less" caveat. You star EpicEng's ride share and undercut Uber/Lyft by a dollar. They respond by matching your price and giving drivers more incentives so they don't switch. Now what do you do?
I can assure you that I do not personally care that people use Uber, but that's neither here nor there. What you describe is not a network effect; it's true of _any_ business you want to see stay in business. If I liked shopping at e.g. Walmart, yes, I would implicitely want others to shop there as I don't want to see them go out of business. That doesn't mean I'd have a second thought about switching to a competitor if they provided a similar service at a lower price.
FB is successful because no one I interact with is on a different platform. They same is true for them, so we all stay. Network effect.
The problem comes with your "a dollar less" caveat. You star EpicEng's ride share and undercut Uber/Lyft by a dollar. They respond by matching your price and giving drivers more incentives so they don't switch. Now what do you do?