I'm wondering if "Sacrifice for the greater good" is so used and Glorified by the Japanese media while the Western Media frowns upon and demonizes it all goes back to the concept of "Ritual Suicide" in the Shogunates.
Back in Feudal Japan dieing for the person/place/ideal you served was the greatest honor a Samurai could have and if one dishonored themselves the only way to redeem the blood and name of your ancestors and descendants was the "Ritual Suicide" technique.
How ever, in the west (America Specifically) there's no honor considered to be in death and suicide is considered the "Coward's Way Out" by many. (Myself included though I wouldn't normal use that exact wording)
So to western and american players it's not unusual that all this "Sacrifice" and "Martyrdom" is being frowned upon and why we are always insisting there were other ways. Because to most of us sacrificing people is never worth a small victory like we've had. G'raha didn't HAVE to lock himself away to control the Crystal Tower, Yasale didn't HAVE to turn into Shiva and ALLOW HER SELF to be taken down (She had given up on living after all), and Minfilia certainly didn't have to be assimilated and/or killed just so hydaelyn could pass ONE message to us that didn't help us one damn bit after we learned it.
All it actually did was make HER ONLY DEFENDERS go "WTF HYDAELYN!?!?" and start questioning their mission. Which would seem counter productive to me.
We can accept Moen to an extent because with out her intervention we likely wouldn't have lived and it was more a "Gotta think fast" kind of thing than premeditated "Since we don't have an obvious better option might as well". Lord H likewise on a spur of the moment "Oh Shit" reaction saved us by attempting to shield us from that potshot and it unfortunately cost him his life. The difference being that for Moen and Lord H there actually was not another option as it was a split second, and quite literal, life or death situation. The other three were not as there were easily more ways to handle the task than "Throw another lamb on the alter".