In the real game, black did use the point lose ko threats and white answer, and black take, and white pass, since there is no ko threat left for white, and black connect. The result is very different using territory scoring or area scoring (the official result is black 3/4 zi equal to 1.5 points, but if using Japanese/Korean rule, it will be W+0.5 point)
I stop at this move just to show the point losing ko threats. Not that it is the final position.
Of course, Japanese rule don’t give black any point for D6, that’s the point of the territory scoring. I was showing this variation to point out that your argument of “One critical property of that is that better territory-score implies better or same area score, so playing for maximum territory is optimal for area score too, but not vice-versa”. Black play C6 isn’t going to maximum the territory but is clearly the case to optimal for area scoring. And the better territory score doesn’t imply better or same area score as shown in the real game.
The whole point of all our discussion is about “Is an endgame ko worth more in Chinese rules than in Japanese rules?”, and my answer is yes. And it has less to do with the “resolution” or “fine-grain” of Japanses rule vs Chinese rule.
I see. We have a misunderstanding. It is my fault for not being more clear, I apologize for not saying this upfront 
But, I am NOT using “Japanese Rules” and “Territory scoring” as synonyms throughout the text. Japanese rules are not equivalent to Chinese rules, of course. But, in whatever ruleset you fix, “counting territory” and “counting area” is equivalent (if players do not pass early), provided that the same and consistent definition for “what counts as territory” is used in both methods. AGA is an example of a ruleset that actually explains how to count territory but get the equivalent area score (and also adds pass-stones to account for the case when players pass early and thus the equivalence starts to break).
Japanese Rules is ONE example of ruleset (the by far most used), that uses territory-scoring. Lasker Maas is another example of territory-scoring ruleset (not used in practice unfortunately), which scores territory much more similar to the “Chinese rules implicit definition of territory” and thus is appropriate for the equivalence in question (as it would count this points).
My intention is to help people who much prefer to reason in terms of territory-counting, instead of area, to understand what is going on in Chinese-rules (and Lasker Maas and AGA) “dame fights” at the end. Using the equivalence, IF you count those points I am saying as valid territory (modern Japanese rules do not allow it, but, it is not so obvious and automatic as you might think: it was deemed valid to keep that point in an important pro game long ago! See the famous Go Seigen dispute ), then you can understand the purpose of the fight and play accordingly: you are fighting to keep that extra point of territory, which requires that you keep the ko open until after dame are filled (that is why it requires having extra ko threats at hand). Also, by counting that point as territory, the previous “rule” I gave about how to convert from territory-count to area-count keeps working. As you showed, if territory is counted not like I say but in the Japanese-rules way, then the rules break and indeed Japanese-territory-count is not equivalent to Chinese-rules.
So back to
This is still valid but only IF you count that D6 point as extra territory for white, in your territory-score. That is not the Japanese way of course, but when I say “territory-count” here I do not mean “the modern Japanese territory count”.
And about
I sort of agree with you here But I also add that, “the reason” why there is more value in Chinese rules, is that Chinese rules “effectively count” (implicitly, by allowing to play there to claim it for free after dame are filled) those extra points inside the ko, if you can hold the ko long enough. IF the Japanese rules also counted those points as valid and allowed you to keep that territory, THEN these final kos would also be fought using dame in Japanese rules. BUT, since the modern Japanese rules do not allow them, then there is no point in the fight.
Hope this helps clear up some of the confusion I probably created here.
I completely understand, we who research into rules, should contribute what we know back to the community, not just for better game play but help dig deeper into the core idea and why till this day, the differences are still not solved in practice. Most adjustments either create too much complexity, or involved multiple phases, or prolong the game unnecessarily just to check some rare situations. Players favor Japanese-style rules might have nothing to do with its fine-grain scoring, but simply because it generally needs fewer total moves to get to the result. The exceptions happen rare enough for it to be practical.
BTW, the strict Chinese rule came from a very different philosophy in finding who is the winner. It starts off as to who owns more than half of the intersections on the board, instead of a comparison of “ownership” between players. It’s absolute, instead of relative. This fundamental mindset is somewhat still baked into some Chinese players (who knew the strict Chinese rule from the start). Even if the “point difference” is like within 3 or 4 points, they would just resign instead of playing it out, and a lot of times lead to sloppy yose, since it is sort of not the point to maximize the point difference.
This mindset of fill out the board in order to compare half of the board, also leads to the idea of using ko to gain extra score to pass the half intersections mark. And interestingly, even if the tactic can be used in situation where one side already has a lead, and still gains extra points, players usually choose not to (since it is extra work to calculate ko threats).