If the visitors land your website after business hours or during holidays and do not get any response they might slip away. They could be important sales leads and losing them can impact your business.
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.

However, if you do choose to do this, make sure you actually follow through and do the thing you’re bragging about, unlike this New York Times reader who was just a bit too bold.
There ought to be a word - and perhaps there is, in German - for the mix of feelings that accompanies composing and activating a holiday out-of-office message. There's smugness, of course, and a gratifying sense of laying down one's virtual tools after a horribly long shift. But for many of us, these nice feelings are tempered by the knowledge that in two weeks, refreshed but depressed, we will have to trawl through hundreds of emails, many of which will be conference room notifications for meetings about crises that have passed.