What are the proven advantages of taking extra calcium?

Goal is 'adequate' Getting an 'adequate' dose of calcium reduces risk of weak bones from osteomalacia. Not sure there is any benefit for taking extra/excessive amts of calcium. In fact, there is emerging evidence that taking high doses in pill form (might) cause increased calcium buildup in blood vessels (bad). Maximizing dietary sources is best. If need supplement, spread dose into 2-3 separate doses thru day.
No need. If you don't have bad bones (osteopenia or osteoporosis) and your calcium level is normal in the blood, then we do not recommend taking calcium supplementation. We prefer you get all your calcium from food rather than a pill and if there is no reason to replace something, there is no need to take it.