Airports are Federally funded, and the people have a right to use those Federally funded assets.
Yup, but I think the situation in the UK is a bit more complex.
As I understand, many airports today were originally built out of taxpayers' money as military airfields during the war years.
Some were later completely sold to private entities.
Some (like MAG), various councils together own a majority of it.
Others (like Luton), the council owns all of it.
Many larger airports have planning stipulations such that they remain certified/licensed as "public-use" aerodromes and therefore must be available to all to use on equal terms and conditions. They also have limitations on noise & movements.
Separate to the above, these airports do feature in regional/national transport planning policy. Some public body decides whether Gatwick or Heathrow gets a new runway having done a study of future air transport - both don't get to expand at the same time.
So (part-)private or public-owned entities as they may be, there is a legislative framework which they operate within. Public / government bodies do have a say in the operations of such airfields and how it fits within a wider transport network, but I think the average bloke on the street is more concerned about noise and environmental impacts.
GA unfortunately does not feature enough in such talks, but there's no reason why it shouldn't in future. So while the lighter end of GA aren’t the primary customers of larger airports, they still have a value and a purpose and therefore should not be seen as a lost cause.
If we don't take part in protecting GA access to infrastructure, the smaller aerodromes will be built over, the larger aerodromes will have exorbitant handling fees and awkward procedures, and airspace will be over-classified to Class A everywhere.