I think this really depends on your role. I don't get enough emails in a day to require 3 hours of replies.

More generally, though, the response can be as simple as "We have received this email; the request will take some time, here's roughly when you can expect an update."

I’ve tried this but then I’m under pressure to get someone a response by a self imposed arbitrary deadline.

I think the cultural norm is to respond as quickly as possible. Realistically that is so challenging.