I agree that it could be worth looking at how school holidays are structured, 4 weeks in the summer (with some overlap but also slightly different times in different areas to stretch out tourism revenue etc) and an extra week in February and October wouldn't be a bad starting point.
The thing is, not all life happens in school. A lot of extra-curricular activities will run special events in the holidays, because they can get the critical mass of children to make it worthwhile. Super-flexible holidays would get rid of this.
It's obviously unaffordable to fund schools opening 52 weeks of the year, but it does make sense to use school buildings and facilities to host holiday clubs. These could be free for children on free school meals, and I agree that more could be done for older children, children with SN, etc, in the holidays.
I do think a lot of people who struggle with school holidays have younger children. For older teens, it's often a time when they have opportunities to do extra stuff, either through their hobbies, or things like NCS, or getting a summer job (yes, older teens do still have these) or just socializing. Perhaps the answer is to have different holidays for primary and secondary schools (although this could become a nightmare when families want a holiday all together). We could also have different hours in the school day to suit the teen body clock.
But complete flexibility just wouldn't work. Currently, the average number of sick days for a teacher is 8.4 (although I'd guess that some are off long term, and others not at all). If full time teachers could take 28 days whenever they liked, that would have a massively detrimental effect on student's learning. They'd regularly be taught by people who didn't know them at all, and didn't know exactly where they were with their class work. It would be an utter shambles (and very expensive to fund).