A general policy of "If you want it bad enough, we'll give it to you" has major costs, actually. In the short term, yes, you're avoiding the loss of lives. Long term, though, everyone knows that you'll give in if they threaten you hard enough, so you incur on many costs or loss of potential benefits.
As a side comment, and I could be wrong about this, but I don't think the Argentinian government has the balls to actually start a war this time. The military is in an even worse state than in '82, and they really can't afford, PR-wise, the comparison with the dictatorship that started the last one. So the cost of refusing to part with the Falklands is limited to economic attacks (like the whole "banning Falklands-flagged ships from entering Mercosur ports" thing). In effect, you're weighing convenience against convenience. Probably.