Uber/Lyft are so much more reliable than a standard taxi. Before the ridesharing apps, I'd had several experiences of trying to call a taxi company to come pick me up (this is in San Francisco). It never arrived after repeated calls to the dispatcher, saying "it's on the way." If they're overbooked, they simply ignore the requests and you have no remedy other than to call another taxi company, which is likely similarly impacted.
At least in my experience, you're not doing either of those things.