Was the Vulcan used because it was a useful way to demonstrate its utility… i.e. the RAF wanted to retain the large/medium bomber capability?
Err, no. The withdrawal of the Vulcan from service had been agreed and planned some years earlier, and I don't think it could have been changed by anything that happened in the Falklands.
If you haven't read "Vulcan 607" yet, I highly recommend it - it's a cracking read and a really human account of the effort that went into Black Buck. You might also be quite surprised at how much the RAF did in the Falklands that one doesn't hear much about, such as the long-range MR sorties flown by the Victors and Nimrods.