I sort of agree on many levels, but don't forget, that like the grey squirrel, the rabbit is not an indigenous species. For rabbits were introduced (albeit several centuries ago) by the last knockings of the Roman occupation as a farmed and controlled food source for their soldiers (as were stinging nettles), and once the Romans pulled out, the rabbits ran rampant (as did the stinging nettles) to the detriment of our native hares and aligned Pagan culture.
In time the rapidly reproducing rabbits pushed our native hares out of most areas, and within the last century, has seen the sanitisation of the traditions and myths of the March Hare get transformed into the sickeningly ridiculous -- and infinitely commercial -- Easter Bunny.
So would I like to see the rabbit population of our fields gone? Maybe not truth be told, although if it could be proven that the removal of the same would help re-establish our indigenous hare in significant numbers, then maybe I would have a second think?
I would loose the grey squirrels as introduced to the U.K. in the 19th Century in a flash, however, as that really would allow colonies of our native red squirrels -- who have been mostly eradicated by the presence of the North American grey -- return to our woodlands (with a little help), as currently they are now only to be found on the Isle of Wight and in areas of Scotland.
Lecture/rant over.