If you're streaming to Twitch, I found I was able to get around this easily by going to my Creator Dashboard on the Twitch website, then using the pop out options on the Activity Feed, Quick Actions and My Chat windows. You can then copy the URL for the each of the popped-out windows and paste them into OBS as Custom Browser Docks.
That's a good point. I figured that out for the chat, but one thing I really liked about the Streamelements integration for OBS was the follower and sub activity. For example if something was broken and you wanted to refresh/repeat an alert on stream, you could just click the button next to the alert and it would replay the alert. I'm pretty sure you can't do that with the OBS Stream Manager, right?