Very interesting. I am not sure the *BSD would like to see themselves as specialists however. They certainly want to be generalist OSes. However, this is certainly a flamewar-like issue, and I do not want to enter into it.
The niche issue is making me think a lot. Are there available niches in computing for the various BSDs? What is the status of their current ones?
OpenBSD selected the security niche. For me, it *seems* that Linux invades it, but that is not actually the case. Linux security is good. But OpenBSD targets paramount security and Linux in general avoids paranoid users. 
The real problem with this niche IMHO is that it does not pay. Funding a big development for security is probably doomed (if someone knows a way, please, contact me directly... ;-).
At some time, it seemed that they also targetted a niche that can be called "networking OS": via the addition of OpenNTP, OpenBGP, etc. Maybe it is still the case but it is a difficult niche too: Cisco iOS is there, as well as many of the networking equipment manufacturers. New big players are either developping their own proprietary solution or starting with Linux which has a good reputation (to say the least) in networking. Finally, like with any other big company, the "security" argument is definitely more for marketing than for real so it is not so decisive...
On the smaller scale, OpenBSD does not seem to want to go on small systems (WiFi boxes, SAN, etc) and OpenWRT&co. is already in that niche.
However, I still think this is a nice idea. Networking is really a place where paramount security would be useful, because it would allow us to forget about it, but not in big networks... Personnally, I would select home security as the niche here (networked home of course;-); it may be the only one that really pays (look at the price of that home alarm system...). But that involves porting to small hardware and well, it seems that's a big step.
There is also potential interaction with mobile devices (smartphone, etc.) - a niche to avoid because of all the predators in it... However, in the longer term it opens the path to industrial control systems and there, the "security" thing could have the same effect as in the home and bring back momentum (only in networking if Linux gets there first as he will probably do).
FreeBSD selected the performance on x86 niche last time I checked. It worked for some time, but Linux is a generalist with a passion for performance too so... Hopefully the niche is big enough for several players to exist. (I wouldn't bet on that, but I am no good investor at all.)
DragonflyBSD selected innovation. Well, nice, while you can have new ideas to innovate with. But no need to worry for the short term: computer science is just 40 years old, new ideas are still plenty. Skilled developpers to implement them are available too (and do not get highly paid jobs in the industry anymore). Passion is a good niche after all (without the drawbacks of paranoia... ;-). Getting out of it is the problem (NB: for paranoia too... ;-)).
NetBSD selected portability. Well, it would be interesting to analyze why it was not selected to be on smartphones and tablets then.
I do not know enough of this OS to speak about it however.
So what are we left with? What are the niches that would allow *BSD not only to survive, but to develop and possibly come back competing with other generalists? At least, that's a nice way to look at the issue. Thanks for the comment.
 Linux with some specific patches does compete with OpenBSD but probably lack the "full OS" and "security first moto" advantage of OpenBSD. (Ouch, I know some other readers will want react to that paragraph: sending to footnote... Please comment separately. ;-)