What you describe is a job that requires a lot of thoughtful, or at least meaningful, answers to a lot of people. If each answer leads to a context switch, this lands hard on any other work you do. On the comms side, this may well be a full time job; or more.
But the problem has nothing to do with email. The problem is with combining what sounds like a full time management job with a full time teaching job. In fact email makes it possible to batch those requests instead of always being interrupted at an external schedule.
And sorry -- I am not trying to tell you how to live your life, what comes next is just an engineering observation. But if one is overloaded the solution is almost always to ... reduce load. Transfer some duties and/or delegate more tasks and/or hire someone to help, etc. This is usually not easy, but IME most folks under overload who say they cannot reduce it either (1) did not try to reduce it in earnest or (2) are micromanagers who are willing to delegate only partway while maintaining the role in final decisions. My 2c.
You're not wrong, but university professors don't necessarily have the authority or budget to hire assistants. And much of the stuff they deal with absolutely requires their unique skills: delegation leads to errors and omissions with serious consequences.
You overestimate delegation opportunities for most teachers. With what money?
As for reducing: research, grad programs, journals, media inquiries - these are not optional for profs
You are accustomed to professional managerial class luxuries that are unavailable to most hard working folks
My mom simply did not respond to emails from students. Or even her faculty. It worked fine for her, except many people considered it rude, but nothing bad happened otherwise. She had an office, an actual one, and whenever it was important enough, people went to the office.