Honestly, HankFrank... I was really more conceding with those others to tone it down some...
Personally, I have contentions all over the place with science's definitions and attempts to quantize boundaries in nature, not just for what temperatures can support this or that in Meteorology, but also, the storms that result them selves...
In essence, I agree with you in whole.
First of all...the sounding structure and ratios of wet and dry air between the ss and the U/A are equally as important in the physics of these beasts. That is why your assertion of mid 70's water has merit... Notwithstanding, storms of lore, such as the "Perfect Storm", this season's Vince, perhaps the event on the Brazil Coast last year in April, these are all quantized hurricane or hurrinace like events that didn't have waters temps of 80 to draw from... But, if you look at the sounding, you'll see that the remarkable similarities - both to one anothers anticedent conditions as well as comparable (by ratio) to the potential instability of a purer tropical sounding...
If all that wasn't enough, the "President's Day Blizzard" of 1979 had and eye, and a quasi-warm core!
Fact of the matter is, there are extremes on the spectrum of storm types that are wholey unique compared, however, the spectrum does not really have a black and white area where you either get one kind or the other.. .i.e, there are warm cores, hybrids, hybrid warm cores, hybrid cold cores and you could define these to Jupiters Great Red Spot and back and still not come up with enough definitions of the storms that can fall in between.
Certaintly a fascinating area of study and I won't bog this page down with Skew-T plots to diagram this stuff, either..

That being said.... Have you seen the 06z GFS! Oh My Goodness... what do we have here... I tell yeah, the GFS tries to do this every autumn in seems... We have Wilma now smartly evolved in the GFS and moving parallel to the East Coast; why, because as we elucidated yesterday, the NAO supported notion of a deeper Ohio and Upper Ohio Valley trough (suddenly, that appears in the overnight runs...) seems to be appearing in the runs. This logically imparts S components along the East Coast. Anyway, the GFS is taking a powerful piece of polar energy and plunging into a closing solution near the New York Bite water area of the N mid-Atlantic, in the area of said trough greatest amplification. This is eerie...because at that time, Wilma is careening N just off shore and appears to be captured by this polar energy, the two phasing, and bombing to 960mb or so in the Gulf of Maine! It's incredible! You think that you have a pure warm core feature being captured by a closing U/A low that almost has winter characteristics for have a core down to like 526dm heights!

But, I've seen this in the last couple of autumns frankly; yet to see this type of exotic phased result pan out. Notwithstanding, the typic huge margin for forecast errors this far out in time, particularly when throwing Wilma into the fray are quite large as an understatement... So, if nothing else, this more for, 'can you imagine if that happened'.