If the typeface actually includes an uppercase and a “lowercase” (i. e., a smaller version of the uppercase, as in Copperplate Gothic), I don’t see a problem. It is similar to setting a phrase in small caps with the initials capitalized: I don’t like it so much either but it is fair game.

Subtle differences in stroke thickness are always expected between uppercase and lowercase, because the uppercase needs to deal with a bigger amount of empty space. Probably it has more to do with the specific case of Copperplate Gothic: specially in lighter weights, the “lowercase” is certainly much more lighter than the uppercase and I would not use it because of that (a personal taste, not a typographic rule). But in bolder weights this difference is almost gone.

Now, if the “lowercase” was done using false small caps, that is a different story, since difference in stroke thickness would be huge (≈30%) and therefore not allowed. The funny thing with Copperplate Gothic is that the “lowercase” in lighter weights is so light when compared to the uppercase than it gives the impression of being false small caps…

What do people think about using the mixed cases in Adobe Trajan? Is it considered tacky or OK? (Trajan now has smaller letters for lowercase). I'm using it for large titles on maps, etc.