I say It's unintuitive because after several hours I found out that the blue circle is the global cooldown for your firesupport.
This was not explained in the lessons and up until now I had to just waited for radio conformation that I could call in a new firesupport.
So there is 2 types of cooldowns: 1 for each individual firesupport (white circle) and the global cooldown (blue circle).
While I would much prefer a minimal UI, this blue circle I believe should be added to the bottom left along the other HUD details. This is because you can't turn left and right when you have the fire support radial menu open - opening it to check how long the cooldown is will risk getting you killed because you can't move your player direction. This is unlike the tactical map where when you open it you can still turn your player left and right.