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But you see how that would result in hostile attempts to claim custody. Often one relative challenges another for custody after its been granted, the trustee often ends up with custody because the demented person insists they are fine, the power of attorney is contested because it can't be proved the old person wasn't demented when they signed it, and then 4 different family members all try to claim custody which is confounded by some of them being beneficiaries of the will.
Someone angry they didn't get anything in the will might try to get power of attorney simply to steal things from an old person's house. Classic shit fight is when assets are missing from the house, and nobody can prove whether it was the old person, a thief, the attorney or the assumed beneficiary who took the asset. People think "grandma left me this in the will and I better take it now before she breaks it". But the attorney can't let them take it, because assets listed in the will might actually need to be sold to pay for the old person's care.
Either you've done this shit or you haven't, and the people who have end up being asked to be executors/POA over and over.