don't see how Archer factors in to whether or not the character Emiya Shirou changes
You're kidding right?
You also seem to be reducing Fate and UBW to the same thing
Because the result is effectively the same? The only real difference is waifu choice and what happens when Shirou dies at the end of his lifespan
it's still a change from his former self-doubt and completely blind adherence to his sense of guilt.
You mean exactly how he does the same thing in Fate? The only difference is he affirms his goal is beautiful with Saber instead of Archer
Fate and UBW would share that development and change, I guess.
Wait what are you even arguing? If they go through the same "change" he has no real added development from Fate. You learn in Fate why he is the way he is, He just denies that it's the wrong way to approach life
aka: The exact same thing he does in UBW
UBW is more about Archer's regret than it is about Shirou's ideal, Therefore UBW is about Archer and not Shirou