I was trained that the compressions are more important than the breathing and if you could do nothing else, do compressions. Theory being that there’s lots of unused oxygen in blood, and by compressing the chest you’ll cycle a bit of air in and out of the lungs anyway.
I was also trained that anything is better than nothing, because if you get to a person who needs CPR (i.e. no pulse or breathing) then that person is essentially dead anyway, and you can’t make them any worse. There’s a good chance that you can make them better though.
Perfusion, that’s what it’s all about.