Which faction do you like the most in Heroes of Might and Magic IV?

So, the amulet will always appear on level 4 of magic. There are 4 of them.

Exactly, the probability of getting the right amulet is 1/4, for Exorcism it's 1/3, and you need both. The total probability is 1/12 - that's not much.

By the time you have, say, 10 phoenixes, I'll already have 60 crusaders.

What's with your math? 10 phoenixes will be added (for a basic estimate) in 5 weeks, 60 crusaders in 12 (a 7-week difference, and that's without losing any crusaders). Do you think your opponent will put phoenixes in at the end of the second month??? No comment.

The Devil's amulet of life is good... but it doesn't really save against angels...

What do you mean it doesn't save? With the same number of reinforcements, devils definitely and easily defeat angels.

I explained about the order.

No, you didn't explain anything. In a game against Order, your mage won't last long (titans, mages, djinns), even after nectar. And the enemy mage will have time to remove everything and add more. Angels will also die very quickly: magic, 1.5x damage from hobbits, and titans. And there are no more units to support fast units.