> Why should anything calling f2 care whether it can produce a warning or not? If the contract is simple - return a value, then that's all we normally care about.

What if you call f2 multiple times? What if you call f2 an unpredictable number of times? What if you call f2 in a situation where the logging system isn't initialised?

The parameters and return value are not the only things that matter.

Simplest situation in order: multiple logs, multiple logs, default uninitialised log behaviour.

These aren't situations specific to the pure/not issue. You have to know how you deal with them in either case. The uninitialised case it a specific case of: what if your logging target goes away / never existed. Signatures won't help here, because that's a dynamic property of the system.