I mean I fully agree with your assessment of async vs sync but conversely I'm less connected to people than I was before. I used to call and chat with friends several times a day. Now almost never.
Another way to look at it, maybe at some point some new tech will come out so thet we don't even talk to people in the same house/building/office. I mean why talk to my sister/mom/dad/wife/son/daughter, they might be in the middle of a thought. I should choose some async method and just never talk to another human directly.
Of course that's ridiculous but if you had told me in 1995 that I'd talk less than a few hours a year on a phone because everyone just messages each other I'd have thought you were describing a dystpoia. Who's to say some new tech won't take it even further.
For in-depth technical exchanges, where conveying the complete picture is necessary before someone makes a return assessment, async provides better results.
But most importantly they differ in how the mind utilizes them.
By default, phone calls (and face-to-face conversations) are synchronous. You call someone, they have to stop what they're doing and have a conversation in real-time. They also can't judge the importance until they're already interrupted and have started the conversation anyway.
Text messages, email, chat and even voicemail are asynchronous. You send a message, the person can respond when able, and likewise. They can also see the initial query, and this can help them decide whether to respond immediately or later.
Async communication has the benefit of being able to work synchronously, if you want, but it doesn't have to. You might annoy people by not responding fast enough, but not in the same way that you would if you were to just put down the phone and walk away for a few minutes/hours.
I think the real problem is misuse of async vs synchronous styles of communication, and knowing when to switch between them.
I personally prefer async communication by default, but if we're going to do near-real-time async anyway, I'd rather have a 5 minute phone call than spend half an hour texting back and forth. I hate unexpected phone calls (and in fact, pretty much don't answer my phone), but I have absolutely no issue with a scheduled call -- that that is usually arranged asynchronously.