I think it should remain there, so you can spy on your enemy, and if you are not careful of when you speak, you will get spied on yourself and reveal your position. So it would be your blessing if you can see the enemy's team messages, but a curse if your enemies have seen your messages. It has been there for many versions to come as a feature rather than a bug.
There is a way to help make your chat (both team and not team) not seen at the top of your head by entering a lot of spaces to the back/front of your message. Or after a message, you can quickly press T or Y and then press enter immediately, so that you'd speak a blank message to overwrite what is over your head, but your teammates still seeing your first message on the console.
I wouldn't mind seeing an option to turn off the words on top of your head though.