Lots of theories. It's not just shad it does not work for, but also alewife and blueback herring.

It seems to be better for Atlantic salmon (57 passed as of June 20 this year), but there are still some big inefficiencies.

One clear problem is the shape of the dam, which results in an attraction flow to the river left side of the dam during periods of high flow (like May and early June when alewife, bluebacks, shad, and salmon are all on the move). The fishway is on river right, and the dam is L-shaped such that fish attracted to spill on river left are ~1500' upstream of the fishway attraction flow on the other side of the river. So they beat themselves up on the ledges below the dam trying to find a passage that does not exist.

But shad have poor passage at dams everywhere on the east coast. Every historic shad river that has had a dam removed has seen rapid increase in shad numbers as soon as the dam was gone and fish could access upstream habitat. The same has not been true when fishways were constructed, and that includes fishways of many different types. Some pass more shad than others, but none of them come close to passing enough shad for meaningful restoration of upstream habitat, especially on rivers where they need to pass more than one dam.

There is a reason the undammed Hudson, Delaware, and Potomac--and now the lower Kennebec, up to the first dam--are the best shad fisheries in the Mid Atlantic and Northeast. All the other large rivers that formerly supported big shad runs--especially the Connecticut and the Susquehenna--have multiple dams. A few fish pass the first dam; fewer pass the second; and when you get to upstream habitat the numbers are very small.

"At first blush I am tempted to conclude that a satisfactory hobby must be in large degree useless, inefficient, laborious, or irrelevant."
— Aldo Leopold