I don't think the issue is team cohesion, but rather level of detail. I'm generally interested in what my coworkers are making, but in the sense of "I want to see a demo of it when it's ready". I really don't care about "Y: wrote DB migration script, T: waiting on design." That kind of thing is neither useful nor interesting if I'm not their manager.

I think people check out in synchronous standups just as much as in async ones. The only difference is if later I'm interested, I can go look it up if it's async.