I don't think they're beyond help, but they're beyond the tweaking and bolt-on new solutions that keep being suggested by politicians and others without a clue.
I wouldn't go private as I think many of the issues in the state sector are found in many particularly smaller private schools (some that are also collapsing) which is what is in my area.
I've home educated all of mine. My DD who is in Y7 this year entered a state school of her own choice and her older sibling will be going to a state college this September for their new KS4 course. I've had no complaints about her school, but like noblegiraffe* said, it's difficult to know how much a game face nice seeming schools are putting on.
I do home educate partially because of how much my local schools are struggling and how much my black spot area (no schools better than 'needs improvement' for many years) seems to be being treated like a testing ground for things that fail: constant new headteachers with new ideas and pretty much everything academized really early (sometimes an infant and junior school on the same site in different MATs). My lodger works at two and he's just been ground down and seeing many of the other staff - particularly TAs, library and tech staff having their hours cut to the bone if not tossed entirely - and kids with SENs being given tablets by teachers who haven't a clue how to use this new fix-all solution has made him start moving towards leaving education entirely.
We've had three new schools in the last 5 years and the two that have had an OFSTED check came out as inadequate, one of those isn't having a new intake this September. We're holding hope for the 3rd which my daughter attends, but it's just a new CoE secondary, it isn't really trying to be anything particularly new or gimmicky and the academy group it's in is just other CoE schools in the same area. While not religious at all, I think the school having that support might help them as all the other new ones were pretty stand-alone even when meant to be part of bigger countrywide networks (the one that isn't taking new students this year used to brag about that).
I think one of the most telling outside of the schools themselves, many which are putting on a brave face, is that my DH works in hospitality and they have had multiple ex-teachers jumping to barely above minimum wage jobs (less than £10 per hour) to "recover" - their word that has come up a lot. One lovely lady came in balding from stress. When dealing with sometimes drunk, belligerent, entitled strangers' safety and wellbeing is the relaxing option, there is a bloody massive problem. Yes, a child's education should be more important than helping someone's trip, but really, hotel work shouldn't be a lifeline for teachers being burnt-out-to-a-crisp, but it seems to be and has for the last few years here. I mean, one of the hotels has been attacked by arsonists repeatedly and it's apparently still better...