Usuallu a cull is done because of disease of over population. They are not suggesting slaughtering ALL geese, and over population of one species can damage the whole balance of the environment.
It looks at first sight to be a case of management, rather than the desire to make a quick buck on goose fat.
If I wasn't human, I'd probably support a human cull tbh, as we're a menace
Windemere is managed, the animals are too, the geese have been attracted there, bred in large numbers, possibly too large and to restore balance the cull is probably the best idea.
Its not nice, but we fiddle with 'the wild', we manage it, and we have to manage it well. Even the horrible bits.