I think clicking the "View older chat" button should only download the last 50 or so chat messages at a time. When you click it again, you can see the 50 chats before that.
I think this is a nice idea which would facilitate the large diplomacy or large FFA games on Multi-day settings. If you feel strongly about this, I recommend uservoice it.
A possible tip would be if you are in a large Real-Time diplomacy/ffa game and you want the chat to remain open, You could open the chat change the size of to be as small as possible and put it to the very side of your screen so you can hardly notice it so the chat so it instantly streams onto the chat and saving the hassle of downloading the chat and potentially crashing your browser.