I will always assume it is an inability to interact in an adult fashion with the world of technology. There is no good reason to avoid voicemails so aggressively – those that are doing so should probably be seeking therapy to overcome their issues with technology and/or the human voice. A lot of us process text faster and more accurately than speech, especially poor-audio-quality speech recorded by someone who didn’t bother to leave all the relevant information. Most voice mails are bad.
Hi, Thanks for your email. You can expect a response when I return on [MM/DD]. Please contact [name] at [email] or [phone] for anything urgent. While you’re waiting, here’s something I made for you: [blogpost, ebook, brochure, checklist, etc.] I hope [name of thing] makes your day a little easier.

I’ll reply to your message promptly, after I delete the dozen email newsletters about losing weight. If your question or request is not time sensitive, wonderful! If you require immediate assistance, please send contact to [insert name] at [contact email].
I might sound nitpicky but the language is important. “Might” or “may be” or “slower than usual” are vague and don’t offer the sender all that much information about when you’re really going to respond to them. Worse, they do a horrible job of protecting the time of the email receiver who, as the responder notes, is not in the office! Such a responder implies that, not only will the vacationer reply to the email, but they may not even miss a beat. They may be slow to respond, but they also might not.