Something has been bugging me for quite a long time recently and I really didn't get what was exactly the reason. Finally, I've found the culprit - it was the window popup animation lag. I've double-checked it with the original X-Com and it was totally missing there - the windows popped up instantly!
Looking deeper into "Window.cpp" I noticed, that such a behavior seems to have been intended, while it definitely should have not. Thus I decided to make a small hack-fix. Of course, it may render some other code in the same file unnecessary, but is to SupSuper to decide.