Then that person is a hypocrite. If they’re expecting responses quickly, but using a medium that’s not designed for fast responses, that’s on them and you should tell them as much.

because they are usually in a meeting and forget to come back to it later

Then ping them again. If it truly is important enough to send an IM over, it’s important enough to follow up after a couple hours.

I’d never even check my email

And that’s why I and pretty much my whole team doesn’t check their email very often. Occasionally there’s something interesting or useful, but almost never. Email is there to broadcast messages to the group that don’t fit nicely into an IM, and they’re usually accompanied with an IM to the group to look for that email.

That’s how every company I’ve worked at has operated. I’m not in sales or customer support, so it’s really not part of my job expectations to deal with email. If something needs to go to another department, it’s probably above my pay grade anyway, so I’ll ask someone else to handle it. I manage a team with almost zero interaction with anyone outside our group, and whenever I need to do something over email, I get explicitly asked to do so (e.g. I had to submit some paperwork for one of my employee’s immigration work, which I did follow up on promptly over email).

We do family reunions every year as well, and those are organized on email, but my parents send a text whenever there’s something important there (e.g. voting on where to go, what to do, etc). I pay attention to the email for the next couple weeks until things get resolved, then I go back to largely ignoring it.

I’m trying to do better about it, but honestly, there’s almost zero repercussions for ignoring it. The things I’ve missed are miniscule to the amount of time I’ve saved by ignoring it.