This is true! The nuclear option also helps the recently returned vacationer understand what is a priority and what isn’t. But, as boyd wrote, “if you just turn off your email with no warning, you're bound to piss off your friends, family, colleagues, and clients.” The blog post offers some helpful steps to make a clean break feasible — they include communicating with colleagues about the sabbatical long in advance, managing expectations of those who rely on you, creating a backdoor for true emergencies, and then, right before going away, reminding everyone about the sabbatical once again.
Voice mail is a strictly worse medium than almost any alternative. You don’t get the opportunity to converse and ask questions back and forth like you do with a phone call; you can’t extract information efficiently from the message like you can with an email (the old “ugh, I have to listen to this entire message over again just to check one thing he said at the end” scenario).

This is the standard reply I’m my org. Occasionally there is something about not being able to check emails while away (or being able to) but that’s about it.
If instead you ask your co-workers to cc or bcc on replies then you will know which have been dealt with. (I think for internal mails it’s more reasonable to ask that if the original person contacts someone else, they cc you so you know who is dealing – and in smaller organisations where people know you personally you could also send a mail round the day before you leave to say you’re going to be out and to ask that any enquiries are directed to [name]in your absence, to try to avoid them coming into your inbox in the first place.