I don't know why schools are blamed. I work for a local authority in Education. Some children, even from starting primary, are lazy and unfit. The number increases as they get older. It is a concern across the country. There have been numerous initiatives but like most things the children who don't need them are those who enjoy them and buy into them and those who do need them, opt out and are supported by useless parents.
By secondary school, core PE is a farce. It's like the Barry Hines film Kes. There are those who love it, take every opportunity offered, are in teams, enthusiastic, generally active in life as well as PE. Then there are those who do very little that is activity in PE and pay lip-service to it they co-operate but walk instead of running, or make very little effort to really learn skills. Then there are those who avoid it - are absent or have a note from home (and every PE teacher gets absolute lu-lus of notes from home with excuses), or forget their kit every week and won't wear school kit, or refuse point blank and would rather get into trouble, or are very overweight and lumber at the back of groups doing nothing with their friend, or waste time messing about instead of taking part. PE teachers manage the ones who aren't particularly good but want to join in - it's the ones who hate it and are really unfit and avoid any physical activity that are the most difficult. Their parents always support them.
I see parents who drive their idle kids right up to school doorways . At work, we had complaints from residents in a street that backs onto a bridleway that parents were driving children down the bridleway in their 4 x 4s to get to a hole in the fence at the back of a local secondary school . We asked a member of staff to check. It was true. Mothers who were driving teenagers who were late, down a bridleway (no cars allowed, not a road) to a hole in a school fence where the lazy creatures squeezed through to avoid staff on late duty at the gates.
Our DC are 4 (almost 5), 7 and 9. They all walk to school - it is about 3/4 of a mile. They all cycle at least twice a week. I walk most evenings and weekends - 5-10K- and they often bring their bikes and cycle back and forwards where I walk. They swim once a fortnight. DS1 and DS2 play football. DS1 plays tennis. DD plays tennis (badly but loves it) and tap dances.
It's a parent's responsibility to make sure their children eat healthily and develop good activity levels- not lie in bed and play computer games in the dark, watch tv, eat crap and get paler and fatter. It's easier for parents to let them do this - and lazy parents who take the easy route end up with lazy, unfit children.
I grew up in a house where no one did any sport but we walked miles and I had swimming lessons. I had to do whatever school decided (my parents just made that clear)so I played tennis and badminton, hockey, netball and lacrosse (hated it), ran round the field, did cross-country (cheated). My family didn't deliberately eat very healthily but compared to what people eat now we were eating pretty healthy food.
Poor parenting is the biggest issue in Education and in children's futures.