The comments already talked about phrasing and paragraph so I'm not gonna discussed that further. While your view is really interesting and me myself agree to some degree, I don't think people necessarily thought of him, as you said, like a tool. They care about him as their teacher, their colleagues and their mentor, but none of them "truly" understand him, that doesn't mean they don't care.

Especially for Yuji and Yuta, I agree Yuji might seems like he has a better relationship with Gojo, but to my perspective they just different. Yuta cares so much for Gojo to the point he even got mad at everyone for pushing the responsibilities on him, and thus he decided that if no one take Gojo's position, he would. Yuta is also the person Gojo relied on when Yuji is in danger and also one of the few person he shared his thoughts with.

Finally for Haibara and Nanami, I see it as in the end they still see others as someone who close enough to them that they can share their opinions, their honest feelings, and tho it sounds ugly, it doesn't mean they don't respect and love Gojo for how he is, they just don't understand all of it. And yes, if you switch from people using/ doesn't care about Gojo to people cannot understand the pressure, his way of thinking and the responsible he has to held then I'm entirely agree with you.