Running an aerodrome takes a lot of work. If this must be paid for, it is either from the users or from a third party. The third party may be a national authority, as is the case for all military fields, or a local authority, as is often seen in France - and also in the USA, I think - with their tradition of municipal aerodromes.
After reading these pages for several months, I am more and more bewildered by the differences between the UK and what I know of the rest of the world. That means mostly my own Belgian country, and a few impressions from France and Italy. English airfields seem, to a large degree, to be operated for profit by commercial companies and these will grab for money wherever they can. Who can blame them? But the scheme seems basically unsound to me.
Over here, most fields are run by aeroclubs, and worked by volunteers. A modest landing fee is general practice for PPL fliers, but many microlight-only fields (called ULM-odromes in our rural south) are completely free of charge, like many are in France too.
If you can't convince your authorities to run aerodromes as public services, the only realistic alternative is IMHO to have them operated by volunteers. Even then you might not get completely rid of landing fees, but at least they might become reasonable.