OP said:
Also, how can this connection work without a longitudinal stiffener?
1) It can work. The coped, top flange-less section just has to be able to handle shear and flexure without over-stress or web buckling at the top.
2) I think that the place to start here is by giving name to the failure mode that we're trying to address to begin with. Then we can meaningfully discuss whether or not the proposed detailing addresses that failure mode. Do we know what failure mode(s) would have doomed the un-reinforced cope?
3) I don't see this beam cope having a shear problem to begin with so I doubt that the intent is to move shear out of the web and into the doublers. And that's good, because I don't see the doublers accomplishing that feat with any efficacty anyhow.
4) My guess is that the plates are specified as a means of preventing local compression buckling at the top of the coped web. And they probably do a pretty good job in that role. You might check this by treating the top of the web as a longitudinal compression member and seeing if the doublers possess enough stiffness to restrain lateral buckling of said, faux column. Given that you're starting with a 1/4" thick web and effectively tripling buckling resistance with the addition of the two 1/4" stiffeners, I suspect that it works. But, of course, all this depends on my having guessed the failure mode correctly.
5) If it were me, and the coped section was really failing, I'd just ask for a longitudinal stiffeners in order to save yourself the time, effort, and uncertainty of evaluating this. Or tell he fabricator that
they have to provide a calc for it and see if that steers them towards a more conventional solution. If there are 10,000 of these things then, sure, put the time in to make each unit marginally cheaper. Otherwise, some mousetraps just are not the worth the effort of bettering relative to the value of your own time.