Gervase -

Did you read that before you posted?
Where do I start?

Obviously the feeling of elation/exhaustion/satisfaction outweighs the feeling of remorse/respect.

You prefer to kill & eat animals that have had a free & happy life than ones that have not. I don't see the relevance, but OK, fair enough, life requires death, go ahead.

"...the cycle of nature; of the link between predator and quarry..."
This is not descriptive of a fox hunt, and besides, calling something natural is not the same as calling it good, or even acceptable. Where I live (rural Australia) Mother Nature is often referred to as "The Crusty Old Bitch".
Tsunamis are natural. Fox hunts are not.

The notion that fox hunting is simply the performance of a civic duty I won't dignify with a response.

"The death takes just a moment"
All death takes just a moment. It's the pain & suffering that goes with it which many people would like to see reduced, rather than celebrated.

"...a game of furry, steaming chess..." Serious? Come on...
I think those who hunt for the sake of witnessing a game of furry steaming chess could almost be sidelined, couldn't they? I doubt we would hear much of an outcry from the furry steaming chess watchers' lobby.

"I can imagine that not one person is there, however, to exult in the death of the fox, or for the experience of seeing it killed."
Well I wonder how the fox would feel about that. The final degradation. After all it's been put through, and for what?

"For many in the modern world, it provides an atavistic chance to connect – to connect with one species hunting another and to connect with a sense of risk and exhilaration that is largely absent today."
Why do we need the connection of one species hunting another? Who benefits? I don't think the hunted species gets much out of it, but more to the point, what does the hunter get out of it? Risk and exhilaration can be found anywhere. Get a surfboard. The only thing hunting provides is the opportunity to kill.

Perhaps you're right. Perhaps we do need it.