I could be wrong, but I think by locak channels, they mean local affiliates. Those local affiliates as well as any other local TV station are what are required by law today.
If it's not required by law and the compensation set by law. Then cable channels will negotatiate and it is very possible if they don't get the deal they want, they would drop the local station.
They would be crazy to drop the local network affiliates - the public would not stand for their favorite shows being dropped. They’d all cancel their cable subscriptions.