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I think the issue of whether or not Izu can come back via backup or be restored, doesn't actually matter so much as the fact that Aruto does not see things that way.

Aruto since the moment he greeted Yui (the Humagear who was working at the amusement park) back in episode 1 has been established as someone who thinks of humagears as people (despite the obvious and staggering number of differences) even in ways other people wouldn't. To him, it doesn't matter if he can just go back to Hiden, whip out the Izu ProgRise Key, and just upload her back into a new body, it's the fact that she "died" that upsets him.

It's like when Nico got infected by Parad's bugster virus back in Ex-Aid, just because Kuroto says she'll be revived as a bugster later (due to her being infected with the virus) doesn't make the dying part magically not hurt anymore.