I noticed an in-game comment from a TPU player a few days ago, saying that it’s not actually necessary to click the 
button to switch teams.
I immediately joined TPU and was able to confirm that it’s usually only necessary to press Enter to go to the team selection screen, then click the AXIS or ALLIES button to switch.
There is still at least one situation where you have to use the button: if you’ve already switched, and want to switch back, but you haven’t spawned yet.
Otherwise you can just hit Enter and switch.