When does a pipe clamp stop being a sensible temporary fix?

For a small leak on an exposed, straight section of pipe, a repair clamp might limit water damage while a permanent repair is arranged. But I wouldn’t assume the same clamp is suitable for every pipe or leak.

How much do pipe material, leak location, and access change whether a temporary clamp is appropriate? A pinhole on a straight run seems different from a split or a leak at a joint, where tightening a clamp could make matters worse. What signs would make you leave the water shut off until a plumber can repair it, rather than try to contain the leak temporarily?