Why couldn’t someone start a marketplace like OmniBazaar, but without any fees?

Someone could, and perhaps someone will.

But, we predict that a peer-to-peer marketplace without any fees would not be successful in the long run. Why would anyone provide the publishing, privacy, escrow, or promotional services necessary to keep marketplace functioning if there were no financial incentives to do so? Computers, hard drives, internet connections, and the electricity to operate them cost money. If there are no rewards for people who provide the marketplace infrastructure, who will provide that infrastructure?

See also the topic "How do I Provide Marketplace Services in OmniBazaar?", and the definition of the term "tragedy of the commons".