So have another column adjacent to the date that stores an enum with an error code with a reason for why the date is missing. My point is, this is business logic, doesn't have a universally applicable definition, and should be handled on a case-by-case basis rather than trying to hard-code it into the date type in the DB.

Default date types, with some columns being nullable, work just fine for my project. I wouldn't want them to be more complicated and force me to consider additional cases, especially if those cases aren't language compatible.