Heroes VII

They shouldn't. It's not necessary to make all creatures of one element the same; that would even be boring. In Heroes 5, the Altegrade unicorns were light unicorns, creatures of light, "subjects" of Elrath. They fit in perfectly.

Anyway, they were just ordinary animals.

It makes sense if mages can summon them, but recruiting them is a bit strange.

Mages summoned Rakshasa in the fifth installment, although this was implemented through building a structure and hiring these Rakshasa.

Mages have never been good at handling animals; they constantly run away from these sadists.

Well, yes, that's exactly why their champion is a magical bird. Of course, we're ignoring the fact that phoenixes are, de facto, closer to elementals than to animals.

What's wrong with birds compared to dragons?

Their appearance. You can create an original appearance for both, of course. However, even stereotypical dragons can look quite cool and impressive. To make a bird look impressive and dangerous, and especially worthy of being the strongest creature of a Faction, you need to put in more effort.