Don't worry ellejay, I'm sure that no one is hostile here - it is just a healthy discussion (and its about time there was one of those in this forum!
) with differing points of view, which I think is the best kind there is.
I do have some points to raise in response to your post though:
Golden Age/Cosy/Manor House and Hardboiled are very significant sub-genres and they are also rather 'pushed' by the course, however I believe it would be somewhat risky to attempt to analyse the crime fiction genre if you only consider these two aspects in isolation and nothing else. It is essentially the reason we are meant to undergo an intense amount of wider (as in diverse) reading of crime fiction throughout the year - so that we understand the intricate ways that the genre has shifted throughout times, locations and cultures.
Also regarding your point on modern texts having stretched the limits too far, that is an excellent one, however I would put forward the idea that no text acts in isolation so that even if you do not consider them crime fiction anymore then they still reflect on what the literary world thinks as crime fiction. Which can be useful.
I'd also further note that the Hardboiled and Cosy sub-genres were not 'the first' and nor did Poe write under them, indeed neither did Doyle. Those both come from a time earlier than Christie and wrote (along with several lesser known authors) in the Great Detective/Victorian sub-genre of crime fiction.