The digital age has made it increasingly easy to avoid people. I realize that the general complaint runs more along the lines of being too easily found, but hitting the "ignore" button or allowing calls to roll to voicemail on one's cell phone is far too easy. We saw a little precursor to this with call screening on the answering machine, back when everybody had a land line phone...before Caller ID. I'm old enough to remember when you had to answer the phone when it rang, just to find out who was calling; the rules have changed, though. Etiquette evolves over time, although I'm not sure that patently ignoring people will ever be considered polite.
When I was in high school and my sister was in junior high, her little friends discovered the phone. We also did not have 'call waiting' then, so if somebody tried to call while the line was in use, they got a busy signal. Our father also had a couple of inviolable rules about telephone use: we had to have his express permission to give out the unlisted home number, and we could not use the telephone after 10 p.m. . Anyone who called after 10 was permanently banned from calling the house, i.e., Daddy would answer the phone, ask who it was, bless them out, and hang up. Being the doc-tor, he rarely answered the main extension, although woe unto you if he did...he was impatient with everyone, regardless, if they were under the age of eighteen. A few of my friends were so intimidated that they'd simply disconnect if Daddy answered.
Of the great many things I wish that I could send to 'core dump' are the phone numbers of several of my childhood friends. The town was so small that there was only one exchange, so for years one had to dial only the last five digits of the number for the call to go through. I can't remember what I was going to buy at the grocery without a list, but I can recite, from memory, about two dozen phone numbers of my various childhood friends.
The other side of this is ignoring personal e-mail. I reserve the right to delete anything that's from a bot or a commercial site, but e-mails from people I know and websites (my various animal rescues, etc.) that I've joined get read. Generally, I make a point of answering them pretty quickly. Allowing e-mail to gather too much dust eventually leads to a jammed-up mailbox and angry and/or hurt friends. Even if it's, "I got it", you should at least acknowledge it- not doing so is the equivalent of burning an unopened letter.
People took the time to call you or write to you because it meant enough to them to do it. Even if you're going to say, "Hey, that's great, but I don't have time for this," at least they'd know not to bother again. Funny how deafening silence can be, when well-aimed.