Did a first aid course recently and again it was discussed.
There is o2 absorbed in the blood, there is o2 in the air in the lungs (16% ish on the way out which is why mouth to mouth works). Also chest compressions will move air in and out of the lungs to some extent if the airway is open.
Our trainer was mines rescue and an ex soldier so had experience of successful (and not, mainly) CPR. In many cases there was head trauma and blood around the mouth. He also reminded us that if you do mouth to mouth you will often put air into the stomach and then when you start compressions they will vomit. Mouth to mouth is then very unpleasant*.
So generally people were put off mouth to mouth or generally confused so did nothing. Compressions only is much better than nothing and much easier to do/remember.
* He had some interesting practice examples. Rather than the clean torso you normally get he had a full sized body, weighted, with hair, glass eyes, blood covered including in the mouth. It certainly made people think and in many cases get confused/distracted even if they were experienced first aiders (with not much practical experience). Also the casualty was never lying on their back in the middle of the room.