That's essentially how I try to use Slack, but when everyone else is monitoring constantly you're simply out of most convos.
That's just how Slack should work.
Ooh! Actually, you can do this already with Slack by choosing "Direct message, mentions & keywords" under settings. Not exactly the same, but it helps.
I really don't get why this isn't the default. It's the first thing I change when logging into a new Slack account.