It doesn't have to be all or nothing, and the current cap on insured deposits is a nice balance.
Small depositors aren't finance pros, they don't have the training or network to monitor bank management, so we protect them from rogue management.
Large depositors can and should worry about their bank's solvency, so we focus their minds by leaving their deposits uninsured.
Unfortunately, when large depositors catch a whiff of insolvency, they don't help fix the problem, they're first to pull their deposits and leave everyone else to pay the bill.
So we should treat them as we treat creditors in a bankruptcy, and claw back the cash they were able to withdraw in the days leading up to the bank's closure.