Football, Cricket, Swimming, Cycling, etc etc are very heavily subsidised and if you take football for example the subsidies from council taxpayers alone would keep many small airfields open for years
Are you sure? I know various sports and their facilities get grants from local and national government, if that is what you are referring to. However, sport like almost everything else is struggling for a decreasing size of the cake. Such support as there is is often on the basis of encouraging a healthy life style through sport and similar activities. Aviation would struggle to make an argument there. The reality is that you have to have a certain income to fly and the perception is that it is an activity for the well off.
The most powerful argument is the economic one, i.e. brings jobs and encourages people to the area. A successful GA airfield will do that to a degree but governments will always ask themselves if money can be better spent elsewhere.