With Uber, there simply isn't an alternative. If they don't accept Visa then i can't use a credit card (or most debit cards, since those go through the visa network too) and there isn't a reasonable way for me to pay at all.
Uber takes Paypal, Venmo, Apple Pay, and Google Pay too. Any would let you use a bank account. You can also deposit cash into PayPal and I think Venmo as well.
They (in collusion with MasterCard) could jack up prices and then there's be an antitrust case against them.
Here's the thing, though - as long as they don't abuse their duopoly position, those anti-trust cases are weaker. And a policy of preferring to side with the customer in these disputes is not exactly viewed as abuse of the monopoly position.