Even in the unlikely case that the co-op could temporally get more customers than Uber, Uber could just artificially lower the prices for customers/increase rates for drivers and win customers/drivers back. A co-op could not do that since they have no money in the bank.

Except when all this happens on an own blockchain where people can invest in the co-op via tokens on that blockchain? Maybe this could even be combined with a prediction market which decides how to counteract attacks (on prices) from Uber?!