Philosophically, why does the death of an understudy kohen allow a manslaughterer to leave the City of Refuge?

Question

Rambam, Laws of the Murderer and Preservation of Life 7:9.

ואחד כוהן גדול העובד, ואחד הכוהן שעבר

[The person guilty of manslaughter -- rotzeach beshogeg -- is no longer exiled to a City of Refuge upon the death of the kohen gadol. This applies whether it's the currently-acting Kohen Gadol, or one who once served in a temporary capacity as such.

This means if any of the following people died, the exile is over:

• The person who was kohen gadol the day of the fatal accident, even if he retired long ago for health reasons (e.g. he developed cataracts)
• A person who was an ordinary kohen the day of the accident; six months later the kohen gadol broke his arm and had to be out for a few weeks, so this fellow served as kohen gadol in an "understudy capacity" for a month, then returned to being a normal kohen when the kohen gadol returned. He dies thirty years after having ever touched the bigdei kehuna.
• A kohen who had briefly acted as kohen gadol at some point before the fatal mistake.

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Okay, now philosophically, what seems to be the explanation given on why the kohen gadol's death helps the situation?

• Gemara Makos 11b -- it's the kohen gadol's fault to a certain degree, "he should have begged for mercy for the generation."

I can understand why anyone who ever touched the bigdei kehuna is expected to feel responsible for the people for the rest of their life ... but how would that extend to that second bullet -- someone who, at the time of the accident, had never been anything other than a totally normal kohen?

Someone on Makos must ask this, no?

(Bonus points -- the Moreh Nevuchim's explanation -- "the people will be united by grief and the blood rage will subside" -- works well for anyone who's ever been kohen gadol; Chizkuni's explanation -- "people will gripe on the kohen gadol for not carrying out justice" ... raises a similar question to the Gemara's reason.)

Answer 1

My premise -- the second bullet -- was flawed: it appears that the only people whose death ends the exile are those who had ever served as kohen gadol at the time the exile was decreed. (And not the time of the fatal accident, but the time of the verdict.)

Rambam Murderer & Preservation of Life 7:10--11 explain that everything is determined by the time of the official ruling that it was manslaughter and the punishment is exile: if there was no kohen gadol in position at the time of the verdict, the exile is for life. Presumably that means that even though they'll appoint someone else soon after. If I'm reading that right, that means that a kohen gadol who began his tenure after the exile started can't end the exile.

So philosophically that works -- if you've ever served as kohen gadol, you're on a higher level of responsibility for the rest of your life. Both vis-a-vis God (the Gemara) and how people perceive you (Chizkuni). Chizkuni's reason fits especially well that it's the time of the verdict, as we're concerned with people complaining about the kohen gadol not carrying out justice.

(With the Gemara's reason that he should have begged for mercy ... you'd think that would align with the time of the death and not the time of the verdict, but until there's a verdict there's no exile, I suppose ...)