Maybe what's needed then is a little 'Info' button (like in 'My Games'😉. That could show the current position, timeout, initial timebank, timebank remaining, who's to move etc.
Also, if you're just browsing games, you wouldn't have to open the whole history window to see if you're interested in looking further at the game, a glance at a mini board might be enough.
If a game is 'Public' then surely all info should be available.