To me, it seems obvious that ground based optical fibres will be cheaper than a space based system by an order of magnitude. So unless say, everyone starts sea-steading and a space based broadband is the only choice, there is no way a space broadband system can really compete with standard ones on earth.
I don't think anyone can give you a detailed answer on how they will make money, because their business plans are their own, and proprietary.
But the premise of the question seems essentially flawed -
There are huge areas of the world that do not enjoy reasonable (or any) broadband access. There are also existing markets for mobile broadband (passenger aircraft, trains, RVs, trucking, ships). There are scenarios requiring broadband access at remote locations where running fiber is not economical or practical (cell towers in rural areas, remote industrial operations like mining, scientific research stations).
Now Elon has also hinted that he believes their bandwidth and costs will allow them to compete with point to point fiber - linking datacenters for example. This is where it might be a bit harder to compete, but it's certainly plausible, especially for certain edge cases where geography and existing fiber runs means a terrestrial line would travel further than a LEO multi-satellite link would. They can, in essence, create virtual point to point links between any two points on Earth far faster than fiber could be run, and much more direct than using existing fibers usually would be.
One useful attribute of any LEO broadband system is agility, where you can deliver the service for the cost and shipping of a ground station. Which means anytime existing providers fail to keep up you have an opportunity to charge a premium until infra structure catches up with user demand. Failing to find useful numbers but the complaint level in Australia around the Broadband rollout suggests a reasonable but not huge market size here.
If the system can actually provide the claimed backhaul levels of capacity the most profitable market may actually be redundancy for existing providers for when lighting strike, lost backhoes etc destroy their connections (or they just want to do maintenance). From the business case perspective this is useful since most of the time you are being paid by a small number of tech savvy customers to not actually carry data which is a low overhead way to run a business.