Suggested by @alxlg:

"News" and/or "Photos" tabs in the main view. The News tab shows all the messages in subscribed channels (public and private). "Photos" does the same but shows only photos (and short video?) from channels but with a more Instagram-like UI. There should be an option to view those messages/photos in their channels.

Of course this is supposed to be optional: maybe add "News" and/or "Photos" from current tabs editor. It would also be nice if Telegram prompt users with many channels with something like "It looks like you subscribed to many channels, do you like to display updates from them in their own tab?"