It's obviously just a step too far to hope that we can privately educate our kids
But it's not a step too far to hope to be the parents who support their children's education enthusiastically, with empathy, time, effort and engagement during the ups and downs. You sound both willing and caperble of doing that by the bucketload.
Nor is it a step too far to hope to be the parents who prioritise the children's need for sustainability of home, education and family unity, over a personal want to stamp themselves a sucess, based on the measuring stick of the past, with the label "provided a private education". It takes letting go of ghosts and self imposed unreasonable expectations connected to a sense of self worth. Which is not easy, but doable when the other side of the equation is given at least equal weight.
And when all is said and done, having been at both private and bog standard comp, it was the children who had the sort of sustainable, consistent, "kids' needs before adults' wants" centred planning and support who had the non shitty end of the stick. In both fee paying and non fee paying environments.
You don't live in your parents' world. You live in this one. The way it is, not the way you (and a great many other people) wish it were. That is not your fault. And there is bugger all you can do about it. Perhaps playing roulette with your children's education as the chip isn't the best way to honor your parents' sacrifices and efforts to get you the education they felt you needed ?
Maybe wanting to emulate your parents is better served by focusing on the essence, rather than the form, of what they did. Which ultimately was being prepared to make the effort required to provide the most sustainable, and supported education experience they could afford.