Reality is they make very little money from GA and would rather they not have to cater for it, but they can make it unviable for GA to afford it. Landing fees can be argued, where having appropriate insurance for the risk, with an army of corporate risk assessors behind them is hard to fight.
TBH most GA users would go to airstrips that the insurer would wince at should you claim damage from an excursion there, our fleet used to be insured for licensed aerodromes only, but we still flew to ALA's. I know of several situations many years ago that the insurers reluctantly agreed to only cover half of damages due to pilots going places they shouldn't be. One refused to cover a kangaroo hit because the aircraft did not do a low pass first to check for animals on the strip, even though another aircraft had landed 5 minutes prior. Pilot ended up out of pocket $25k or so.