I work in IT support and get tickets sent to me. I review the ticket when it's sent to me as soon as I see it to determine if I need to make myself available straight away or not. If I don't and it's for something minor, I often leave it open for some time, because these tickets already have estimated dates on them and I still get back to the client within that time, however in doing so at least 50% of these tickets resolve themselves or the client forgot they even logged one in the first place.
If it was more urgent than it seemed at first, the cilent will chase up and then I will get back to them straight away.
You say my time is not more valuable than there's, but my time at the role is purely on helping others, so responding to someone straight away or not has nothing to do with me deciding if my time is more valuable than there's, it's me deciding which client deserves my attention the most at this moment.
There is no 'my' time when I working in a support job because all my time is already on helping others.