I don't think I could see him seeking it out. Like, if he happened to get thrown back in time to WWII, do I think Shirou would kill Hitler given the opportunity, probably, yes. But he wouldn't actively seek time travel to do so or anything.
I'm not even actually sure if I think he'd choose to do so if the opportunity presented itself. I kind of compare it to his decision to save Sakura in HF, rather than kill her and make sure she doesn't hurt anyone else: it was the choice between this definite, tangible person in front of him, or the possible faceless masses that he might never see. Shirou's desire is more about seeing people happy, so he doesn't do the same "just save the greater number of people" thing that Kiritsugu does.
I see him as thinking that it's fine to regret the past, it's fine to think about the past, it's fine to be driven by the past, but ultimately, what happened, happened, and that's what made the world the way it is now. All those people that weren't saved, it would have been nice if they'd been saved, but they're dead, and a dead person can't be saved. Even if you changed the past and made it so they never died in the first place, that wouldn't change the fact that, in one place and time, they died. Instead, you'd just be changing the facts of the situation and pretending it was never anything different, pretending they never died or suffered, which is the same as saying that their death, their suffering, their life had no meaning worth acknowledging. So saving them would be equally meaningless, and Shirou can't accept something like that.
The defining events of Kiritsugu's life were the island and shooting down the plane. When he chose not to kill Shirley, and then saw everyone he knew die and the island he called home burn, that forced the idea of "consider the outcome of what you do" on him, so he weighed the possibilities and considered how many people would live or die based on if he killed this person. Then when he shot down the plane, he killed the only person left who had any attachment to him, and cemented the whole thought process in his head, such that even with the image of his wife and daughter right in front of him, the abstract six billion humans in the world was more valuable. He winds up living a bit in the future, constantly thinking about what will happen after he does this thing.
Shirou never had those kinds of decisions until the Grail War. For him, he doesn't usually think about the consequences that will follow what he does beyond "will this save these people here?" What comes after, can be dealt with after. Shirou lives in the present, and focuses on who is here, now, in front of him. People need saving now, why would you worry about people who already weren't saved or who might not even need saving? And that's the key difference between Shirou and Kiritsugu, really.
I don't think Shirou ever even considered using the Grail to save the world or anything like Kiritsugu did. That's why his partnerships work the way they do, because he has no interest in obtaining the Grail. The little bit of selfishness that you could say exists in his wish to save people, that he wants to see the people around him smile, actually grounds him, where Kiritsugu's desire to save humanity detaches him. Shirou wants to help people, where his father wanted to save humanity.
This is probably rambling and confusing. I should probably sleep.
I'm not even actually sure if I think he'd choose to do so if the opportunity presented itself. I kind of compare it to his decision to save Sakura in HF, rather than kill her and make sure she doesn't hurt anyone else: it was the choice between this definite, tangible person in front of him, or the possible faceless masses that he might never see. Shirou's desire is more about seeing people happy, so he doesn't do the same "just save the greater number of people" thing that Kiritsugu does.
I see him as thinking that it's fine to regret the past, it's fine to think about the past, it's fine to be driven by the past, but ultimately, what happened, happened, and that's what made the world the way it is now. All those people that weren't saved, it would have been nice if they'd been saved, but they're dead, and a dead person can't be saved. Even if you changed the past and made it so they never died in the first place, that wouldn't change the fact that, in one place and time, they died. Instead, you'd just be changing the facts of the situation and pretending it was never anything different, pretending they never died or suffered, which is the same as saying that their death, their suffering, their life had no meaning worth acknowledging. So saving them would be equally meaningless, and Shirou can't accept something like that.
The defining events of Kiritsugu's life were the island and shooting down the plane. When he chose not to kill Shirley, and then saw everyone he knew die and the island he called home burn, that forced the idea of "consider the outcome of what you do" on him, so he weighed the possibilities and considered how many people would live or die based on if he killed this person. Then when he shot down the plane, he killed the only person left who had any attachment to him, and cemented the whole thought process in his head, such that even with the image of his wife and daughter right in front of him, the abstract six billion humans in the world was more valuable. He winds up living a bit in the future, constantly thinking about what will happen after he does this thing.
Shirou never had those kinds of decisions until the Grail War. For him, he doesn't usually think about the consequences that will follow what he does beyond "will this save these people here?" What comes after, can be dealt with after. Shirou lives in the present, and focuses on who is here, now, in front of him. People need saving now, why would you worry about people who already weren't saved or who might not even need saving? And that's the key difference between Shirou and Kiritsugu, really.
I don't think Shirou ever even considered using the Grail to save the world or anything like Kiritsugu did. That's why his partnerships work the way they do, because he has no interest in obtaining the Grail. The little bit of selfishness that you could say exists in his wish to save people, that he wants to see the people around him smile, actually grounds him, where Kiritsugu's desire to save humanity detaches him. Shirou wants to help people, where his father wanted to save humanity.
This is probably rambling and confusing. I should probably sleep.