Surely the main problem is not with the qualification but the fact that there are multiple exam boards, each one a private company. Why do schools go with one over another? To get better results so that they are bumped up the league tables. And so we have a "race to the bottom" where the exam boards are lowering standards so that more schools pick them over the others.
Keep the GCSE but have one state-run exam board.
You can't change something and keep it. If they were to change they way GCSEs work, then there would still be a difference, but things become muddy if the name sticks. Pupil from year X gets 9 GCSEs, Pupil from year Y also gets 9, but somewhere between them the standards were changed. How do you compare the pupils?
compare that to: Pupil X get 9 GCSEs, Pupil Y Gets 9 O-Levels.
Much easier to compare.