I can only speak for myself - I produce exec/board materials. Often a request will go out to several people and I can get ahead by responding first. Sometimes someone will reply to me quickly and the edge I bring is properly digesting their response and then going back quickly to them with questions. Others might accept they have a reply and then wait until they are pulling the paper together to realise they are missing key data.

I don’t read or action all emails instantly, but I am very aware of the ones I need to, or when I am in a period of high focus that needs information fast.

In an ideal world I’d be in an office with all the people I needed around me, all with the same focus and priorities, but that is rarely the case. So to excel at my job I need to make connections fast and respond fast. (Note this isn’t just email, this is just for my communications in general.)

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.

I remember one event vividly.

Exec asked for some business information information while traveling.

I replied promptly, sending a link to a webpage, within the proper process for secure data sharing according to company policy. This required exec to visit our internal website to view the information.

A teammate emailed the information directly, violating policy and good data stewardship.

CEO replied to teammate's email with a big group thank you for "emailing the information quickly".