I think you are confusing "monopoly" and "barrier to entry". "Monopoly" would imply some state where every person using your system makes it harder on your competitors. If, however, your system needs to reach a minimum level to be useful, but doesn't have a feedback loop above that--you have a "barrier to entry"-a fixed cost that must be paid on entry to the space, but doesn't automatically get bigger when your competitor adds customers.
AirBnB doesn't really have a monopoly but they do have a barrier to entry--they perpetuate mostly by continuing to turn a blind eye to the violations of law. If someone stood up a site and used VC money to reimburse listers in New York and San Francisco, AirBnB would lose most of their revenue and you'd have an Uber/Lyft duality. The barrier to entry is that they are already in the space and there doesn't seem to be enough money floating in the space once laws start getting actually enforced for VC's to be willing to throw money into the ring.
Uber and Lyft also have a barrier to entry--a network of drivers. I can pop open the Uber application and know that there is probably a driver within 5-10 minutes of me. Nobody other than Uber or Lyft has that coverage so I'm not going to use another service. Could someone else build that network? Yes, they could--that's a fixed cost that must be surmounted, but once on the other side of that cost adding more drivers or riders doesn't really have an effect that makes it harder on your competitors.