You've got it backwards. Congress has effectively delegated its power to issue debt to the Treasury. That would ordinarily be unconstitutional. But the Supreme Court has authorized such delegation so long as Congress provides an "intelligible principle" by which the executive must exercise the power: https://en.wikipedia.org/wiki/Nondelegation_doctrine. The point is that Congress ultimately remains in control.

The debt-ceiling is what makes that whole exercise constitutional to begin with. Congress said: "okay, Treasury can borrow money, but only up to this much." If the executive disregards the debt ceiling, that would break the fiction of delegation, and the executive will have fully wrested a fundamental Congressional power away from Congress. That's the same reason why the 14th amendment cannot override the debt ceiling. Yes, the debt ceiling is a statute. But without it, Treasury has no power to issue any debt.