It doesn’t have to be ‘immediately’ useful, it doesn’t have to be useful at all. But, if we are to care about truth, we care about truth FOR some reason. The question “why do I care about Truth” presupposes that it might be possible to answer “I don’t.” So it is not intrinsically necessary that we care about Truth, so it is up to us to justify our desire for it.

I think truth is useful to many people. You want your romantic partner to truly love you, you care about the truth of their feelings. Many examples where we care about truth. So then how do we get truth? You’re right, an inexact but working model of it is the best we can do. Thats what I was also getting at with my idea that we don’t care so much about absolute Truth, but only subjective truth.