This is partially a request for opinion, and partially a request for statistics.
For a very long time, Meta Stack Exchange has suffered from a problem where a lot of users ask blatantly off-topic questions here, such as programming questions. One of the reasons for posting off-topic questions here, as pointed out in my answer and Tim Post's answer, is that users follow a link here, not realize they've been directed to a different site, and then ask their (off-topic) question here.
Both answers were posted during a time when each site had unique design elements. Even then, users would go to another site, not realize they've been cross-linked, and ask an (off-topic) question. Now that many more site design elements have been standardized, it's possible that this could become a far more common occurrence (not just for Meta Stack Exchange, but for all sites). Even as a seasoned SE user, I've occasionally missed that I'm on a different site when I've navigated between sites where the new design has rolled out.
To be honest, this is my only gripe towards unifying site design elements; otherwise, I'm all for doing this if it means that the code base is more maintainable.
Is my analysis of this issue correct? Would having unified design elements result in more off-topic questions from lost users? Has this actually happened? Finally, if so, what can be done to reduce the incidence of lost users?