That is, with summoning magic, you can summon a phoenix with parameters higher than a non-summoned phoenix. ... I looked at the latest save, and what do the parameters of the summoned phoenix depend on?

The summoned phoenix has little in common with a regular one (just as the death avatar of necromancers has nothing in common with a summoned dragon), it does not resurrect after being destroyed (at the same time, the hero who summoned it completely loses all his mana).
And the parameters of the summoned phoenix are determined by the level of magic of the hero who summoned it, and they are almost always higher than those of a regular one.

And you don't play as the High Elves out of principle?

I play as all races, but I prefer Warlocks :)