I agree, things like this should be implemented, or at least the ability to minimize pop-ups. I play with minimize pop-ups until the end, but I still find that they pop-up when I feel it isn't the end yet, and get in my way. This happens especially when I need to check other things in order to determine my choice, like tech choices, and some construction choices.
I would REALLY like an option to have things stay minimized, so I can choose the order I do things, or ignore them until I deliberately activate them. This is always a major problem for me in multiplayer, where a turn can end at anytime, and if I get a special event pop up at the beginning of my turn because I have no movement, I often end up making a choice on accident without having the opportunity to read it, because I was trying to do something else (more often than not, talking to other people).