Everyone thinks that their inquiries are urgent, top priority. That's not always the case, it maybe urgent to you, but not to the other person.

If something is critical, you can communicate via other means: phone calls, SMS, slack, etc.. and even then, there's no guarantee you will get a response.

In business context, I lean the other way, tend to give all parties as much leg room as possible.

I think The Eisenhower Method is a great fit for prioritization.

Airbnb recently sent me a terms change email that doesnt apply for six months and I dont use it anyway, but email headers set it to urgent and important.