...Especially when they fight Phoenixes, which always get the first strike. In the case of the Black Dragons, it's also the last strike.

The biggest weakness of the Black Dragons is that you can't add any enhancements to them. A Phoenix, with its cat-like reflexes and first strike... or under the effect of a Dragon's Strength spell... or under the effect of everything at once, will easily defeat a Black Dragon without much effort. Not to mention the fire immunity of the birds, which reduces half of the damage dealt by the Black Dragons. And who is stronger or more useful of the two?
I absolutely agree.
The fact that they are immune to magic in some cases is not a plus, but a minus.