In windsurfing some people recommend board straps to be setup in such a manner that foot is only partial trough strap and only part of the bit toe is visible on other side. Logic is it easier to take foot out of the strap in emergency. So straps are setup quit narrow so foot stopped from going in all the way.
Talking about TT boards mainly:
My kitesurfing instructor said foot should be well in - all the way basically and quit firmly.
In my very limited beginner experience such setup might make it more difficult to get rid of the board in emergency so I am not 100% sure this is best.
Some people here suggest very loose straps - so foot can even rotate inside straps.
What do you think is correct setup is? Loose/wide? (for TT riding and/or for freestyle/jumps - could be different I guess).
I think your intuition is correct. The worst thing that can happen in straps is one foot in and one foot out.
There are two ways this can happen.
1) the straps are so loose that the foot can rotate inside the strap. In a hard landing this means that one strap can get around the ankle. If this happens you can not get the board off the foot because the board twists locking that one strap in place. Very dangerous! Do not make the straps so loose that the foot can rotate.
2) the straps are so tight that you can't get the foot out. You are kicking and kicking to release the board but nothing happens because it is so tight. Now if you are doing handle passes you will need the straps to be incredibly tight so the board doesn't come off but ok then maybe you should be riding boots.
So just make them medium loose. That's how most people ride anyway.
Now there a few riders that suggest super tight --- these guys are doing handle passes or megaloops, you don't have to imitate them, or they are doing board offs. Board offs, you want the straps super loose, and the way you look the board on your foot is by pinching your foot against the strap, but it's not optimal for safety because the board can lock in place around the ankle, but if you are doing boards off I do recommend them super loose, just makes it easier to do the trick just be a little careful if you think you are crashing the landing to kick the board entirely off.