Until recently, the misfortunes of regulated cab companies — and their dwindling profits because of ride-hailing services — drew the most attention.

Uber and Lyft in America, Didi in China and other ride-hailing firms elsewhere have used sackloads of venture capital to drive down fares and flood the streets of big cities with cars, clobbering the earnings of licensed rivals.

Now, the losses of the ride-hailing services themselves are in the spotlight. In a filing released in the run-up to its initial public offering, Uber said it has lost $7.9 billion since 2009. Lyft, which listed last month, lost $2.9 billion in seven years. Uber is seeking a valuation of up to $100 billion, but as yet it is unclear if it can make money.

Start with Uber’s most oft-touted attributes. Its name has become synonymous with ride-hailing. The company claims to have more than 65% of the ride-hailing market in the United States and Canada, Europe, Australia, New Zealand and Latin America. But it sees itself as more than just a taxi company, with car ownership and public transport in its sights. The proposed valuation implies a huge market that Uber would need to all but monopolize.

Look through history, though, and taxi monopolies look anything but impregnable. Len Sherman of Columbia Business School draws a parallel between Uber’s business and that of unregulated taxis in New York in the 1930s, when Ford’s Model T emerged as a new, low-cost cab. During the Depression, many jobless workers took to taxi driving, undercutting each other. The streets were saturated with vehicles but the earnings of drivers and taxi companies evaporated.

Uber and Lyft are reprising that episode as they fight city by city for drivers and customers. And customers throughout the decades have proved they care little what company provides the service, as long as they get from A to B. That means neither firm can easily increase profits by raising fares.

Uber’s long-term goal is autonomous vehicles, which would reduce its need to share revenue with human drivers. The market has potential, but other companies are keen to enter the fray. Uber will surely have a place in the future of transport. It may be able to increase rider and driver loyalty by replacing fares with monthly subscriptions. It may settle for dominating some cities, leaving others to rivals, provided that does not violate antitrust rules. History, though, suggests that profits will be hard to come by. But at least its name will likely live on.