It would be wonderful if all state schools were excellent. However, human nature, as ever, intervenes. Parents have very varied attitudes to child rearing and very varied attitudes to priorities. Maybe its a UK thing or maybe its more of a universal aversion to being told what to do, what is the 'right' thing. Choice exists. It would be very worrying to remove it.
As to improving state schools, increase taxation? carry out all the various forms of social support that are talked about all the time, tackle gang culture, sort out drugs, so much to do before thinking of abolishing schools that just quietly get on with providing education for those who choose to prioritise it.