I haven't answered a single phone call from a number I don't recognize for years now. As far as I know, I haven't missed anything important.
When the doctor's office can't get a hold of you, now you're looking at 6 months longer until you get to see the specialist you've been waiting for.
When probation can't get a hold of you, now you're looking at an unannounced visit, violation, and/or arrest warrant. This happened DAILY when ankle monitors suddenly malfunctioned and communicated that they'd been cut off or that I was violating home confinement by leaving unannounced.
But that's just my experience I guess.
related, i found out within the last month via mail, after-the-fact, that Progressive had canceled my car insurance due to a billing change, and so i couldn't legally drive that week. you'd think an insurance billing department of all places would leave a message if they can't get hold of you immediately, but nope. not their policy. i guess the spammers have ruined things so much that if Progressive did leave a message most people (myself included) would mistake it for a phishing attempt anyway.
One thing I really noticed was the dramatic drop in call volume once I stopped answering calls. Once I stopped answering, they stopped trying to call. People are basically being trained not to answer the phone.
Agreed, though, "don't try this at home" should be emphasized more.