I am a sports photographer.
You learn pretty quick that you do not run from an on coming play. You run at a 45 degree angle in the direction of the play, but off to the side of it. This allows you to put distance between you, but also keep you eye on them. The play would have to make a significant course change to hit you.
Otherwise you might get run down.
Running with your head turned like that would generate a big pull through your fascia and mess with gait, proprioception, the vestibular system, etc. Is 45 degrees the practical limit for that, besides just keeping your eye on things?