I can see two main solutions here.
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Random. Sometimes Crushing blow requires Ancestral power, sometimes Demonic. On the other hand, why bother with the system at all then? It only adds RNG.
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Tiered affixes.
(a) Like 1-5% crit chance do not require any ADA power. But 6% crit chance affix requires Angelic Power or whatever. That way, if you want that last step on the affix tier, it comes with a cost/tradeoff, but you can do perfectly fine with just the second highest affix tier too.
(b) An alternative to this version would be scaling affixes, if you have 0 Angelic power, the affix gives 3% crit, if you have 30 Angelic power it might give 4.5 crit, if you have 60+ angelic power it might give 6% crit. That way, you have soft scaling instead of hard breakpoints. Both systems can work imo, just a matter of preference.
In any case, yes, it would be really bad if each affix is tied to a specific ADA power. That would be D3 sets all over again. By locking players into a few pre-defined paths of where they can go with their builds.