Ok,
I need to qualify this by saying I've never ridden an actual tri-bike but I do participate in triathlons, have seen hundreds of tri-bikes and my road bike has been altered some to make it more like a tri-bike (but pretty minimally).
When I first put aero bars on my road bike I was wobbling all over the place. Steering is much different and the maneuverability is not as good. I would say that this is the main disadvantage.
As far as comfort goes it's not a clear cut answer. Once you've become accustomed to it, riding on aerobars is much more comfortable than riding in the drops. Depending on which route I take for my commute, I'll have a 2 to 10 mile stretch where I can just put my head down and go, -only having to slow down a few times. In that kind of riding, a tri-bike will be more comfortable IMHO than a road bike.
If you think about ironman triathlons, -these folks are riding over 100 miles after swimming 2.5 or so. Then when they're done riding, they get to look forward to running a marathon. I don't see how you could do that on a bike that's really uncomfortable.
As much as I like riding on the aero bars, I don't do it in stop and go traffic, not only because I don't have quick access to the brakes, but because it's not worth the effort to get into that position if I've got to get out of it a block later.
As far as dealing with rough roads goes, I don't see how they'd be any better or worse than a road bike with skinny tires. My last triathlon was on mostly good roads but part of it was cobblestone, parts were rough and there were a few small potholes to avoid.
The last problem is the expense. Most of the road bikes I see people commute on are pretty old. There are exceptions of course but in this town if you only counted bikes that were 5 years old or less the percentage of road bikes vs other types would be much smaller. Most people don't want to spend that much money on a commuter.
So the bottom line is if somebody were to give me an expensive tri bike with the only condition being I had to commute with it as well as race with it, I'd give it a shot. I'd sure like to have one to race with and it would be fun to commute on a few times too. In the end though I'd probably end up giving the bike back.