truly generic problems -- i.e., conditions that might apply to any resource on the Web -- are usually better expressed as plain status codes. For example, a "write access disallowed" problem is probably unnecessary, since a 403 Forbidden status code in response to a PUT request is self-explanatory.
If there is no information in response other than the error status code, there is not need to return a Problem Details body in it. The response code is enough.