Claiming this in general is trivially rebuttable by the fact that I know many people who feel precisely the opposite: if it's important you call, if not you text.
If anything, that view is less irrational than yours: a mode of communication that's immediate, loud, sustained for many seconds, and hits a device that most people have on them constantly fits far more easily with realtime urgency than any other mode of communication.
On top of THAT, there are still stupid legacy systems (that are nonetheless important) that use old forms of communication. My insurance was cancelled while I was on a backpacking trip and they called me and sent me a letter without bothering to send me an email. The fact that Blue Shield are fucking idiots doesn't change the fact that I was without proper medical insurance for th rest of the year (due to ACA enrollment limits). I could easily see the same being true of phone calls.
It seems to me I can either call, which most likely causes a loud and persistent ringing noise that signals "someone wants to talk to you right now, please pick up the phone". Or I can send you a text which will make a quick beep on your phone and then go away.
I actually adopted the "don't answer the phone" strategy about 20 years ago, when first I got voice mail. I wish everyone had. But nowadays I don't even listen to my voice mail.
I wouldn't say I'm cautious, it's simply that if it were important, why would you call?
I basically consider phone calls as unimportant as paper letters. Check in on them every few weeks.