I have actually been kind of bothered by this. I'm so used to the chat function being usable throughout the entire match in most games (except when loading a new map) that I find myself trying to open the chatbox during cutscenes. I like to tell everyone gg after rounds or give people on the other team a hard time for losing, but I cant do that in this game and it's kind of awkward. The chat setup at the end of rounds is probably the worst part about the system though because not only do you have to switch over to another page to view it (why the hell is XP the first thing you see?), you have 3 separate tabs for it when it should just be one window.
...I really think this feature could use some streamlining and I'm just going to point to TF2 as an example of how to do VOIP and chat correctly.