Upgrading Great Hall awards classic arena tourney points.
Let me start with im probably the big dumb for not knowing sooner. However, i've only just recently started playing this game smarter and not as a time killer, so my initial lack of care lead me to not reading many informative parts of early game.
Currently though, the game still makes no mention of gaining points this way, the info just says you only gain points by winning offensive matches. Plarium, what the hell? Thats some basic level information to leave off.