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Replying quickly looks like you care and you already know what's going on. It also suggests that you'd be willing to have even more synchronous conversations (phone calls, trips together, etc.)

Doing it during business hours matters more than off hours outside of major deadlines or event prep.

With many organizations, if you want to give this impression and also shut down communications to focus, you need blocks of time outside of business hours where you focus. For example, I know a responsive executive who cannot be reached from 6am-9am every weekday, when most people aren't trying to get hold of him. This is when he writes and reads. Even then, his assistant fields communications so he doesn't seem to have disappeared.

Not saying you should do this or that it's for everybody.