Just reheating a topic from 1.5 years ago, where back then someone already complained that this hasn’t been implemented in the last 1.5 years. So after 3 years, here goes nothing:
Text chat interrupts the gameplay flow. No matter the game, and also in Enlisted. You must stand idle in order to chat and most situations do not allow for such vulnerability.
The only time that truly lends itself to composing a message is when you are dead and waiting until you can play your next squad.
And it is at precisely this time that the text box gets hidden behind the squad selection, and that you cannot open the chat to write.
The suggestion is to simply move the chat box to a visible spot, and to assign the “enter” button - or whatever you have set text chat to - to opening the chat box for you to write something in it on the respawn screen.