This idea was considered in the past, however the sidebar provides helpful information to "watermark" screenshot and video ban evidence. This information helps us find faked evidence much more easily. However, I do understand that it can get in the way sometimes. My method for avoiding that is changing my GUI Scale to "Normal" instead of "Auto" in the Minecraft settings; this gives you a normal-sized GUI, but if you make the game window bigger, it doesn't automatically make the GUI huge to match.
Here's how my Minecraft screen normally looks (I have the game set to be a 1280x720 window, since my screen is 1920x1080):
We might look into the possibility of offering a "minimize" solution, removing as much information from the sidebar as possible to make it as small as possible (and maybe compacting the timestamp to something like "6/8/15 14:33", but ultimately the timestamp and server ID must remain for the reasons I stated.