Since you asked why not, I will tell you why not:
1. Loss of lateral stiffness, due to the extended unsupported length of the the stay/shock unit. There is a reason bikes of this design (http://www.bikepedia.com/quickbike/Bike ... +Ti+Amp+FS
) went away! You would basically be rolling your bike back 15years, technologically speaking!
2. At a minimum, it will require a lot of labor to make some sort of custom machined fitting to connect the shock and stays in a way that has even a semblance of stiffness, so basically, a lot of labor to end up with a mediocre result.
Having said that, if you just feel like messing around and having some fun with your bike, it is worth considering the following....It is a little tough to tell from your bottom photo exactly how the the shock eyelet and end of the seatstay are configured. Having said that, I would imagine that if you really want to do this right, and as you say, eliminate movement at that eyelet, you might want to take a few ideas from current model Specialized bikes that use yokes attached to the back ends of the shocks. The problem is that, if memory serves, many of those simply rotate the shock shaft in the body 90degrees, so that the eyelet will only pivot side to side, not fore/aft. If you were to do this, it would compromise your lateral stiffness even further than it already is.
Also, I think that many of those DT shocks that you picture use spherical bearings in the eyelets, making it even tougher to get any stiffness out of that connection.
If you really just feel like messing about with the bike, you could craft some sliding delrin blocks, that would brace the seat stays against the seat tube, like on the early Intense M-1s before they added in the swing links, which would add some stiffness back in.
It could be fun to mess around with, but if you really plan to ride the bike, I am guessing you would finish the modification, ride it once, and then put it right back in the stock mode once you see how poorly the new setup rides.
BTW, if weight savings have anything to do with this plan, ditch that quick release seat clamp, strip the paint off that frame, swap any remaining steel bolts to ti...and forget about swapping the shock unless you find a lighter one that will work in the stock configuration with the swing link.