I have no problem with Harriss using Propp to show how House is structured like a cop show... But I would not call such an argument a work of genre analysis - it's a study of narrative structure drawing from textual traditions tied to specific genre categories.
Am I just mincing words to police a boundary here? Perhaps. But I try to lay out this distinction on pp. 18-19 of my book: there is a crucial difference between studying genre categories and genre texts. Analyzing the genre category is to understand the meanings and assumptions linked to the genre, considering issues like perceived core attributes, cultural functions, target audiences, and social worth.
I would hardly argue for a Proppian textual analysis, but I wonder if the kinds of textual readings that scholars have typically performed on genre texts don't start from a different epistemological vantage than historical, industrial and receptive constitutions of a genre as object of study. Mittel is certainly right (if I'm reading him correctly) that textual scholars don't start with a blank slate. When Joyce Nelson proposes a reading of Mildred Pierce as overdetermined by the competing stuctures of film noir and women's melodrama in the text, she activates a prior notion of what film noir and the women's film are. And yet... neither film noir nor the women's film were genres that circulated in any self-conscious way among audience at the time: at best we can say the industry worked with some proto-generic understanding (often with different labels and categories, as Steve Neale has shown so well with melodrama) of how formulas were to be put in place depending on subject matter. It has been the work of critics to read retroactively into bodies of texts, to unearth structured meaning, to find regularized conventions out of the industry's formulas, to make genres out of cycles.
Of course that is not all that scholars do. We also look, in objectivist fashion, at the industrial history of cycles and generic terms or, in subjectivist fashion, at the way viewers themselves understood and made sense of generic categories, So I'm not extactly disagreeing with Mittel: what I do in my own research is to trace out the historically situated circulation of social problem films as "social problem films". But I'm wondering if retroactive critical practice might not be seen as a more separate activity than more widespread genrefication. And do a genre's core attributes ever clash with perceived core attributes? It's a genuine, not rhetorical, question I have.