Any improvement, for instance from reducing administrative overhead, is a gain. Would you reject a 25% cost reduction, because it isn't a 50% cost reduction?

No, but that isn't the question. Would I implement a proposal that only resulted in a 25% cost reduction if I needed a 50% cost reduction to pay for that proposal? The answer to that question is no. I can't afford the change if it doesn't yield enough cost savings.

With single-payer, you get a modest reduction in administrative savings - but it's small enough that you still end up having to impose very large taxes or very large provider reimbursement cuts in order to make the math pencil out. Since neither very large taxes nor very large provider reimbursement cuts are politically feasible, that makes single-payer politically infeasible as well. You can't get that partial gain (lower administrative costs), because that partial gain requires a massive change to the system that is too damaging to too many people to be adopted.