I'm not sure what the goal of that would be and it seems like it would be taxing on the service, if your target audience is global. Asynchronous platforms make sense in a lot of ways, but I am not a strong developer and just speculating from my own experience as a user.

What are your thoughts on what the benefits would be to having all users active only during certain hours?

Having real time interactions gives a very different feel, it's a little like entering a local pub with bustling activity I guess. In my university years I used an anonymous social app called jodel that would show recent posts in your area. And it kinda had this special vibe, everyday around 8am someone would post a weather forecast for the day and people would greet each other and this type of stuff. Having everybody on the same timeline makes interactions different. And you can have real-time conversations too, which makes me less prone to endless scrolling and more proactive in my use of the app