I write Jack Shafer: Who is an appointed populist? "[S]elf-appointed populist" is a snotty remark signifying nothing. Riley is no more a "self-appointed populist" than you are a self-appointed press critic. Sure, Slate employs you, as Fox employs Riley, and readers of my self-published web sites and books read and elect me.
I don't recall the term "self-appointed" ever imparting meaning.
I'd say that a person like Riley who creates himself may be more worthy of admiration than those who are placed in their positions by large bureaucracies such as CBS News.
PS Yes, "self-appointed" gets used on me all the time and I'm sick of it.