FYI, you can click the board to make the arrows disappear while observing; not perfect if you're trying to kick back and just watch but good enough 
Nice work on tabbed design! (and a feature request)
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Glad you like the new design.
We intend to add a way to hide arrows. Not sure exactly how it will look like, but we will take this suggestion into consideration.
Hiding team chat, but allowing observers to see arrows is just the current way things work. Many people seem to like to see the arrows while spectating (me included) and at the same time do not mind if their arrows are shown to spectators when playing. Instead of thinking if it is consistent to hide the arrows or not, I think it is better to think whether people like that feature or not.
I've just gotten through (hopefully!) one of those crazy-busy stretches of life, and had to put a lot of rec activities (like 4PC) on hold.
One nice aspect of this is the singular jump in features/enhancements... I wanted to give an immediate kudos to the development team on the tabs! That rocks!
And as promised, a feature request:
Under the Settings tab, would it be possible to have an option "Hide arrows when observing".
"Optional", as I'm sure many players are comfortable enough with arrow-drawing conventions that they add to the experience of observing. But personally, I just find it really distracting when I'm trying to assess overall position of each team and "random" arrows just keep popping up on the screen.
An aside: for those who are enthusiasts of this feature - isn't it a tad inconsistent with hidden team chat? That is, if insights into each team's strategies and plans was meant to be part of observing the game, why not show the team chats as well? How is observer to know if, right before an arrow was drawn, the teammate had chatted, "Don't do this!!" ?