i don't care
Earlier i was playing a game and trying to click on enemy heroes to find out which one had a gem. During this time i was getting spammed by chat boxes covering up the inventory of the selected hero down in the corner. Consequently we were getting pushed hard down mid lane and trying to figure out who had the gem took more work than holding the lane.
My suggestion is to have the chat boxes default position pop up just above the interface where the opponent inventory is displayed (among other things when clicked) to avoid any covering up of inventory, or wasting time clicking the boxes away.
ugh.. I can totally relate to the chat pop-up box popping up at the wrong time. Sometimes it pops up just as you are clicking and opens the 'f6' window. This might be at a crucial moment and can be very frustrating.
Moving it up might not be good either, because you might be trying to click on the map there..
Maybe create an option to have the 'you have 1 IM' notification etc appear in your in game chat instead. So that it wouldn't be 'clickable' and hopefuly wouldn't interfere with your vision too much.
Or even just an option to disable the visual notification, so that you can just press 'f6' when you want to check, or just listen for the audio notification.
Have the chat box pop up where the scoreboard shows up.