Our company has a similar number of channels, if not more, and you don't scan all of the channels for input. People typically subscribe to their team and related team channels as well as any topics of interest. Slack makes it easy to bring someone in just by mentioning them, so people get added to the places they didn't know about as needed.

Once you start seeing that you're subscribed to too many channels, you just leave them as they lose relevance to you. There's even a middle ground where you can mute notifications from a channel, but can still watch what's going on.

The main problem with slack is the poor search capability, and that's very relevant to your comment.