Zodiark was a bit more than a tool, they literally poured their tears and souls into him. Zodiark represented their hope in front of the final days.
Both Hydaelin and Zodiark are "Her" and "Him" with a capital H, but we have to remember the text is primarily wrote in Japanese which doesn't have such a thing. Although they do have honorifics.

I would add that, the plan has always been to summon Zodiark and then bring back the souls once saved. Letting the first step happen if she didn't want the second would obviously cause issues.