While most contracted, FFD airlines could certainly negotiate with their mainline partners in order to increase wages for their pilot group, the disadvantage they have over, say wholly-owned carriers (Endeavor, Envoy, Piedmont, PSA), is that the parent company does not have the same vested interest due to their business model.
Look at, for example, SkyWest - they fly for Alaska, American, Delta, and United. Increased pilot compensation without a decrease in profit means negotiating with four mainline partners. Moreover, SkyWest is a publicly traded company accountable to shareholders, so operating as lean as possible is even more important. They're not going to increase wages unless it's absolutely necessary to fill classes.