I would get behind this, though in my head the successor lens I was picturing is slightly more modest:
EF-S 15-60mm f/2.8 IS USM
Actually, it could top out at the current 55mm and I'd be happy with that too. The difference between your range and mine is an extra zoom factor (4x vs 5x), which I think ends up being pretty important to the design of a constant f/2.8 lens (somebody correct me). I mean, if you think about it, f/2.8 zooms currently can only do about 3x or less, regardless of format:
Nikon 14-24 f/2.8, 1.7x
Canon 16-35 f/2.8, 2.2x
Canon 17-55 f/2.8, 3.2x
Canon 24-70 f/2.8, 2.9x
Canon 70-200 f/2.8, 2.9x
An f/4 zoom is better, but still only the newest one hits your requested 5x ratio:
Canon 24-105 f/4, 4.4x
Nikon 24-120 f/4, 5x
Envelopes are meant to get pushed of course, but going straight from 3x to 5x for fast pro glass is asking too much at once, I think. I would imagine your lens to be closer to $2.5k than $1.5k even as a non-L because of all the large and exotic glass/fluorite elements you would need. Make it "L" and it balloons to $3k and gains another 500g at least. And who knows what kind of distortion and/or vignetting you would get anyway. And god forbid the flare resistance could be even worse.
The current 17-55 doesn't focus especially close IMO. If the MFD of the successor is similar (likely), I don't see much benefit for including an H-IS design. It would probably be even more expensive and fragile to boot. (You want another reason for repairs?) Even the new no-holding-back EF 70-200 f/2.8L IS II doesn't bother having it. I don't think anything other than lenses designated as macro will ever get H-IS. Maybe if Canon gets a manufacturing breakthrough, but that's pure chance from our perspective as customers.
Now, if your 14-70 was f/4, though, then you have something there. It would be what I think the 15-85 should have been. I would have bought that in a heartbeat, even priced at the 17-55's level. f/4 vs f/5.6 is something I can really feel at the tele end. I can give up one stop for tele (and "get it back" from the 7D sensor), but not two.