Matspart3
I understand what you say and I must admit that the financial situation of many airfields is a strong and valid point. However, when one wants to buy/sell a business there is an entry in the valuation of the business, this is Good Will, usually it worth a lot of money if you can demonstrate that you have it.
Look at the free landing as a P.R exercise If you help someone when he/she is most in need, that person will never forget it and come back in a better day to have your cakes and tea, if you will not help, it will be the other way around.
We are talking about small number of landings and the lost revenue is minimal.
Regarding the abuse, you always find some people that will destroy something good. The only way to stop it is buy charging and letting them know that they did not fool you, at the end of day (I’m not a solicitor) you have the right to refuse free landing if you are not convinced that it was a real emergency or diversion.