The person arriving without an appointment may have exhausted the routes that require one.

Turning up unannounced looks like a failure to follow the process and is more often the end of a long attempt to follow it. Phone lines that ring out, forms needing a reference number nobody issued, a portal that will not accept the details. By the time a person is standing at a desk without a booking, they have generally tried what was supposed to work.

If you deal with people at a counter, ask what they tried before they came rather than what they should have done. And if you are the one arriving unbooked, saying plainly what you already attempted usually helps.