To the owner/operator, nothing.
The whole reason for the FSC coming into being in the first place was many shippers and carriers had contracted rates set in place, but rising fuel prices rapidly made those contracted rates unacceptable to the haulers of the freight. The contracts couldn't just be willy-nilly altered, so the addition of a surcharge for fuel was added, with the surcharge itself being tied to the price of fuel. Without the FSC, no one would haul their freight for the outdated contracted rates.
There are some accounting issues for how companies record FSC, even for those who bid on freight with a flat bid, as well as those bidding out the freight. Some account for FSC as overhead expenses, for example. So while a load may be bid on as all-inclusive, the winning bidder may very well break it down artificially to a more normal rate for the contractor (unless the contractor is paid on a percentage, then maybe not), so they can account for a certain percentage of the revenue as being separated out at line haul and FSC.
A carrier will get loads from bid boards, just like someone with their own authority does, and it's bid on a flat rate to haul the freight, then some of the revenue gets broken down artificially into the line haul and the FSC, even though one lump sum was bid. There are some bid boards where a carrier will bid the line haul, and then after the bid is won, a FSC is automatically added based on the contracted FSC rate they already have in place with that customer. NLMI is like that with some carriers, where the carrier may bid $1 per mile, and then after the bid is awarded a contracted, pre-determined FSC rate gets thrown in. Let's say the contracted FSC is 14 cents. The bid that gets placed is $1.00, but NLMI sees $1.17, so it's not like one carrier is bidding a $1.00 against everyone else who doesn't have contracted FSC rates who are bidding $1.20 or so. (The numbers are fictional, and should not be confused with real numbers, living or dead).
So whether you're shipping or hauling, the freight all gets bid on at basically the same rate, which is what it takes to haul it from A to B. The FSC is then separated out, either up front or at the backend, for accounting and distribution. Some carriers have to deal with FSC, some don't. But to the owner/operator, all that matters is the total of the line haul and the FSC, and whether or not it makes the load profitable.
When they make it a law that 100% of the FSC must be passed on to the contractor, then with many carriers the FSC will simply disappear. That way they only have to pay whatever-percentage of the FSC (which is what many of them do already, especially those with flat-rate FSC, like FECC).