Due to listing rules, US exchange listed options may only be traded on an options exchange registered with the SEC.
All of the exchanges currently charge a fee per contract. Some (maker-taker exchanges) offer a rebate for posting in the book, which depending on your broker, may be passed on to the end-customer.
If they did not do this, but instead charged a fixed amount per trade, a customer could put in a marketable order for 10,000 contracts which would have to be executed on whatever exchange is at the NBBO at the time. If that was only an expensive maker-taker exchange charging $0.90 per contract, the broker would have to pay $9,000 for the trade.
While exchanges may not in fact charge this much (their fees can change monthly) and a customer may not be able to open a position of 10,000 contracts (due to maximum position limit rules, or adequate liquidity) you get the idea that if the broker could offer trading of options on a per-trade basis, they could lose money. As a result, they have to charge per-contract. Some brokers offer cost-plus pricing, where you pay a fixed amount plus or minus whatever the exchange costs or rebates.