This resonates with something I noticed in client work. A surprising number of "urgent" requests resolve themselves if you wait a day - the person either figures it out, realises they asked the wrong question, or the underlying situation changes.
The tricky part is building enough trust that people don't feel ignored. I've started replying with "I'll look at this tomorrow" rather than going silent. Same delay, but it signals intentionality. People seem fine waiting when they know you've acknowledged the request.
Though I'll admit the line between strategic delay and just being slow is thin when you're managing multiple things at once.