Power of attorney is personally determined by you, someone you trust will handle things as what’s best for you and what you want, prior; and different for every individual.
Did I imply otherwise? It is prudent for any adult to designate their POA desires, document them, and inform relevant family and friends in case the need arises. In cases where no POA has been designated a parent/guardian, spouse, etc. may end up having effective decision-making regardless. In some cases the state will decide. This is nothing new.
So you really want medical professionals or some “political professional” to determine if you’re sound-enough to vote?
If I have Alzheimer's, dementia, or other mental incapacitation I would want my POA designee to manage my affairs including removing me from voter rolls or simply preventing me from voting. It is the sane and pragmatic thing to do. If a person has not "gotten their shit together" before such an event (designated POA) or has never been in control of their own affairs, then some other authority, be it doctors or state actors should decide.
Is this where you’re really going with this?
Yes. You fail to realize that in many cases the important decisions that drive this whole discussion
have already been made by the individual who failed to care for themselves, failed to plan for future events, or some combination. A person who has untreated mental illness and who has no personal support structure (family, friends, insurance) should become a ward of the state, not left out in society to fend for themselves--something they clearly cannot do.
Some of these conditions are reversible (homelessness, addiction) and others are not (Alzheimer's, dementia, psychosis, etc.). A person who is in a dysfunctional state of being has no business voting or making any other important decisions. That is all.