I gave it a 9. One of my favorite 3rd season episodes and very good overall.
I think I would have had Kirk et al grab a few disks each before beaming out, since they had a moment to chat there before beaming out. Or while McCoy & Spock are having their exchange and Kirk is off camera then he reappears for the beamout with an armful of disks.
My thoughts were along this as well. To me the whole episode has this feeling of urgency. I once got a chance to keep any book in a library of the Naval Air Station in Guam when it closed. After I got that option I just felt overwhelmed. So many books, so little time. And that is how this episode felt.
In later Star Trek series maybe a wide beam could have beamed a lot of that library up, but in this series not as much.
But I think I would have at least grabbed the desk viewer and the other discs since the civilization no longer needed them.
Kind of a nifty idea...escaping destruction by going back through time..but how'd they discover time travel before interstellar spacecraft?
Why does a Vulcan revert to primitiveness simply by going through time?
Heavy use of Hodgkin's Law of parallel planet development too.
I basically thought a lot of those thoughts as well.
As for "Hodgkin's Law" what if it only looked like a Musketeer time frame from Earth? Or at least that is how Kirk's mind interpreted those events from his own experiences? At least I think that is how things would check out with people in real life. They would enter the strange place and be able to see what their experiences and knowledge allowed them to see.
And in a scene left on the cutting room floor, Kirk learns that the "Atavachron" is really a Matrix-like VR. Everyone who was "prepared" was really digitized, their bodies destroyed. In the accelerated time of the VR, all the refugees manage to live out subjectively full lives before the whole thing is vaporized by the nova. Hearing of Spock's behavior, Kirk decides not to inform him that he fell in love with one of the few computer generated "bots" left over from the VR development phase.
That is interesting and seems more likely for this non-star farring society. And also explains why the librarian stayed to the last minute. Of course, maybe the librarian was lied to by the government to believe he was actually going back in time when it was all just a VR computer. At any rate, virtually he got to go to a heaven of sorts.
The Remastered effect just lays an explosion on us, matter-of-factly, splat ... it's crass, crude, and goes completely against the mood. What I especially hate is that they ruined what I've decided to regard as the final moments of ST (TOS).
Indulge my little mental rearragement of all this please... I like to think of AoY as the finale to season 3, after which came all the summer reasons, then in the Fall, a premiere episode of fourth season that never was, Turnabout Intruder. It was shown right when the next season was starting... I remember Shatner talking a bout it on Mike Douglas or something, by the way, how they'd show TI just before going off the air permanently.
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Anyway, what a great moment to consider the finale of ST.
You like considering Star Trek going off in a bang? Understandable. Transformers Season 3 (classic) did some creative re-arranging of their episodes over air dates to make for a better story. And I agreed with their assessment.
I think I could agree this was indeed the best end for Star Trek season three.
As for the supernova effects, which you can see side by side here:
Simple yet poetic for the original. Star gets bigger, the planet winks out. Nice!
Remastered, Star explodes, material and nova effect quite nice, the planet is wiped out in the shockwave. Also nice.
I think one thing about the Remastered effects verses original is that remastered considered scale and distance. So you see a ship on the view screen in remastered and it is tiny.

You see the planet as they warp away getting distance and it is tiny. But in truth, it would have been tiny.
Oh well, I like both. For the episode I'd give it a 8. Was an interesting concept, and like I said left me a feeling of loss. A whole library with recordings of history, and there was no way it could have been explored in three hours even if they all didn't get zapped to two points in time.
And in the end, not much is known about that world before it is destroyed. They had a ice age, a musketeer-like age, and sometime in the more modern times they had a dictator that liked to banish political opposition to weird points in history. Then the sun was going nova, so they digitized their people.
And here is the most interesting thing of all. People traded their corporal state for a chosen VR environment. What an effective way to effectively commit mass suicide. Once digitized they were stuck in the VR. When the world was destroyed, so were everyone in this VR world though presumably they were able to live out their lives in this VR state. Time being relative within the VR world.
So the world was ending, and rather than have people rioting and looting, they offered people an "escape". And EVERYONE chose that over the horrible reality they all faced ahead of them. There was no request of the most modern history. A history with a dictator? Can't say I blame.
A government offering VR life of happiness in exchange for a voluntary death. Fascinating.