There's a difference between a cameo and an actual character that plays a role in the game.
Statistical differences does not equate to "important" statistical differences. In a conventional game where Marth, Sigurd, Celice, Leaf, Roy, Lyn, Eliwood, Eirika, and Ike are all playable, they're not going to be able to each stand out in their own way either in terms of gameplay or in terms of personality.
Looking at the relevant characters on your list, you noted two characters as balanced, three as overpowered, two as just bad, one as fast, and ignored the last one. When considering that Sigurd is simply better than Celice, the only characters who could possible stand out, according to your own words, are Sigurd, Ike, Lyn, and Eirika, and I don't think there's any dispute that when placed next to Sigurd and Ike, Lyn and Eirika are not going to stand out.
Now, a conventional game is already basically unfeasible for this purpose, and we can't assume the characters will keep their exact distinctions. But let's be serious here. Sigurd and Celice. Marth, Roy, Eliwood, and Eirika. What would could possibly give each character in those groups something important that the others don't have? And by important I mean something out of: skills, classes, useful personal weapons, events, availability, massive differences in relevant stats. In a way that provides a unique advantage for each of them - Eliwood's Knight Lord class provides a unique advantage for him compared to Eirika's Great Lord class (eventually), but not for Eirika.
There's another consideration to take into account, now that I think about it: the timing of when the game is set relative to each of the characters' stories. Are they getting magically transported out of their story before their quest even begins? Or are they returning as confident heroes at the end of their stories (which of course is bad news for Sigurd). It wouldn't matter much for a more fighting-based game with less story and character development, which would be easier to fit outside of canon anyway and perhaps have more opportunities for the characters to have distinct skills, but again, it limits options, and to the sorts of games not all FE fans might like.
While they seem to counteract what HM is supposed to be, it's certainly not as if they're so ridiculous as to cancel it out entirely.