It's a hard decision for the many parents for whom it's a marginal decision.
In the end, it can never be about a broad state vs independent choice. It can only be about you weighing the costs in terms of lifestyle impacts now and in the future (think pension implications possibly) against the likely gains your child will receive from a particular school.
All of the decision making is based on partial information. You can't know for sure how your child will do if they remain in state, nor exactly how an individual school in the private sector will pan out for them. It is hard to know if your child will access all the many extra curricular opportunities available or refuse to join in. It doesn't matter if lots of children at that school are in the National Youth Orchestra or playing for the county or getting a full sweep of A* grades and going to Oxbridge, if your child isn't going to do any of those things (although all those things probably create a positive atmosphere) when you are interested in what your child does.
All you can do is gather as much info as possible. Know as much as you can about the state options and outcomes (with an open mind - some can be excellent) and know as much as you can about the independents by really drilling down into the glossy marketing - so find out exactly how many are involved in different activities, how many take the subjects your DC might be interested in, performances of both the high end and the lower end too, destinations after school if all children, not just the elite etc etc. And you have to know your own child and be realistic too, as far as possible. Know their personality and whether the state school will enable them to thrive or not (of course many children do thrive in all kinds of state schools and some children are more able to do it than others) but also if an independent school will really make much difference for them (some will be hard working and motivated wherever they go) or if the wider opportunities are likely to be accessed or ignored.
In the end, I think many people feel the decision is marginal. They think their child will have a bit better experience and do a bit better at an independent school, and know the fees they paid were huge and possibly too much really for the gain (although this is relative of course to the sacrifice involved and that differs a lot) but they chose to pay that expensive price for the small gain. That's fine if you can pay the big price and not be ruined by it. If however, it means no pension, and no holidays for years and worrying about the boiler breaking down, then I really think the cost is too great.
But lots of us will choose to pay a high price for a pretty minimal extra gain, because of a gut feeling that education is worth it, and our children are worth it and that minimal gain counts for more than an extra bedroom or new car or great holiday or couple of extra years in retirement.