That is because there is a cost associated with renouncing US citizenship. You'll get hit with an exit tax on all your assets, making it extremely painful. The US really does not want you to renounce, because then they can no longer tax your global income.

They essentially punish wealthy people (financially) for renouncing.

You actually don't have to prove anything, you just state that you paid taxes and how much you paid (if taking a foreign tax credit). As for rebate, that is something else, meaning those taxes were already withheld by the IRS for some reason.