Nobody knows who he is or where the photo was taken, so it's hard to see the problem with posting the photo.
Should your neighbour read this forum then he will obviously recognise his own garden. What do think his reaction would be? Do you think he'll be pleased to see his garden being described as derelict, his beekeeping described as substandard? Obviously not. That you can't see this makes me grateful that you are not my neighbour.
Much of what you write doesn't ring true with me. 1 or 2 swarms every week over the summer? Unlikely, swarming usually ends mid July. Garden unusable for 1 to 2 hours. Again, unlikely, a swarm lasts probably 20 mins max. Far less disruptive than a bonfire.
Most beekeepers aim to minimise swarming since there is a financial cost to it. Now there are some beekeepers who don't do any swarm control (I am one of them), but these tend to be the eco warrior type. They wouldn't tend to use polystyrene hives (the small green ones in your photo).
The hives are not neglected. They are new (not cheap), have feeders on them, and the comb left on the top of the hives looks like it was built in the feeders (so obviously well fed).
There are 3 full size national hives in the photo, with a further one stored at the back on its side. The entrances have been reduced to a very small size, that doesn't fit with a hive that has swarmed 10 days ago.
If you are calling other beekeepers to collect swarms then what do they say? Surely they would have given you the same advice that you've received here? Do they report on the temperament of the swarms they collect? Are these 'angry' bees to them? Are they not getting fed up of collecting swarms if this is a regular occurrence?
I worry about the impact of my bees on my neighbours, but stinging or swarming are not my concerns. It is noise. 8 hives generate a lot of noise, yet you don't mention this at all. Last summer I went up to 10 hives in my garden. Standing in my neighbours garden apart from the noise you wouldn't know there are hives in my garden. Bees fly up and well over head height. Growing a hedge or planting trees is the most sensible advice you'll receive. In the big scheme of things is little monetary cost (a few tanks of petrol).