OP, ultimately, unis can only deal with those who actually apply to them. What matters more than percentages of this sector or that sector are the offer rates for individual unis and courses. As long as these are consistent for applications across all education sectors, then nobody is at a disadvantage.
Cambridge did a lot of widening participation initiatives in recent years. They used to publish their results in the format of offer ratios to the 'independent sector, ''maintained sector,' 'other' and 'overseas.' It became very evident that most of the offers within the maintained sector were going to those at high performing grammars, other selective state schools or super-selective state schools like Brampton Manor. So now, you will see the stats for 'maintained sector' includes a breakdown for grammars, comprehensives, sixth form colleges snd FE colleges. Offer ratios for grammars and independent schools are quite similar. Offer ratios for comprehensives are slightly lower and FE colleges lower still.
They are trying to attract more applications from under-represented parts of the country, eg. the NE or Scotland. But they can only deal with those who actually apply.
I remember seeing some statistics that if all A stars at A level (in the U.K.), just under 30% are achieved in the independent sector. Top unis admissions should reflect this (and now do). I think at Cambridge now, 75% of students are from the state sector (albeit mostly gramnars, etc).
Once they get to uni nobody cares who went to whatever school anyway.