At first, some people will be offended. "Why didn't you let me ping and buzz you and interrupt you all day? You didn't respond immediately each time :'((". Some people with unrealistic expectations may even stop talking to you entirely.
But eventually (years maybe) they will get overwhelmed too. No one can handle this madness indefinitely. I've seen giga-texters get broken down and turn into lazy texters like me, or at least learn to tolerate my long response intervals and recognize it as a coping mechanism rather than rudeness.
I have a list of ~10 people I would consider "close", immediate family and good friends, and 5 or 6 more tertiary contacts. I travel fairly frequently, so I had plenty of opportunities for sending postcards. I send cards for obscure holidays just because. The physical process of hand-writing messages is so therapeutic for me. I've probably sent ~250 postcards in the last year and a half.
I have received... 3 physical responses. It has been extremely disappointing, but I continue to send mail because I enjoy the process of writing the cards, and the knowledge that people probably appreciate the mail makes me feel good, so at least I get a little out of it myself.
My mom will occasionally text to say she liked the postcard, but has never bothered to send one back to me.
I would be delighted if more people chose to communicate slowly.