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The chance of Necromancers getting diplomacy is 4% higher, but only for Priests.

4% is a low probability, even though it's almost the same for everyone.

Also, regarding joining for gold, a lot depends on the power you have, and as I understand it, not only the quantity but also the type.

This exists in the physical game; you're not saying anything new. I tested it, and very few join for free. Test how well diplomacy works for Necromancers, test it.