You argue that the airfield would benefit a "tiny" number of people to the detriment of many. Consider that any installation, apart from a supermarket, directly benefits only a minority. But that isn't a reason not to build playgrounds, libraries, caravan parks, climbing walls, etc. We live in a society of individuals, of beautiful diversity, which means that we see different things and different people around us - we even get to try things we wouldn't normally do once in a while. This is why you should not oppose a few technical enthusiasts on the basis that there are only a few of them.
And as for the noise, you must do your research. Many light aircraft are very quiet (consider motor gliders for instance), and they fly considerably further from you then, say, a car on the road next to your house. You can indeed measure noise to back up the case.