We live in complicated times. Prorogations. Constitutional crises. It is not surprising, therefore, that the government wants to talk to the public about simple things that “make sense”. Unfortunately, the education policies of the two main(ish) political parties may be feeding the anxious political climate.

Take the battle cry of the education secretary, Gavin Williamson, who has set a target that vocational education in Britain will “overtake Germany” in the next decade. It is not clear what he means, but British politicians have been saying this since 1868, when Matthew Arnold, inspector of schools, first mentioned it in his reports.

Almost every politician who drifts into education compares the UK with Germany – and usually promises “parity of esteem” for technical training, a vacuous phrase. Given our fractious relationship with Europe the comparison is goading, designed to tap into a latent dislike of other nations, a fire that does not need stoking.

Instead, he could have argued we should become more like Germany. But that might involve confronting the cultural and economic reasons why Germany is so much better at non-university routes – for reasons ranging from industrial relations to the structure of the economy. What it doesn’t involve is yet another press release announcing this year’s “biggest reform in a generation”, while delivering a few tweaks to qualifications and some extra cash.

Things are no better in Labour’s corner. While Angela Rayner, the shadow education secretary, said last month that she would “end tax loopholes” from which private schools benefit – a good idea – Labour members went further, endorsing a plan to redistribute the schools’ endowments and properties to the state. The #AbolishEton campaign was born.

This smacks of the same naive and aggressive politics as Williamson’s. It would be legally tricky to achieve, with some arguing that it could flout human rights. Remember most private schools are not Eton, and a number exist to cater for small religious minorities.

Furthermore, while private school alumni are over-represented in top jobs – judges, cabinet ministers, senior journalists – this is changing. Cambridge’s intake is two-thirds state-educated, while the latest intake of MPs overwhelmingly attended comprehensives.

We need to keep focused on the bigger point. The critical problem is that the rich hoard educational advantage. Abolish every last private school and it will make no difference in most deprived areas, because there aren’t fancy schools in them, or – even worse – because rich people will buy houses near the best state schools and continue educating their children in a closed circuit, this time on the public purse.

Given all that, and the amount of time and political capital that abolishing private schools would soak up, it would be better to think about another plan.

Why not follow the path taken by India and force private schools to take 25% of their intake free, and without any academic selection, through a random lottery anyone can enter? The state would pay the standard amount for each lottery place that it gives local schools; the other 75% of places could be charged for at any rate the school wishes.

In a swoop, the exclusivity of private schools is burst open: no bans and no legal contortions. If that is not enough, push the percentage up to 50%.

That might feel uncomfortable for both sides. Those who want to get rid of private schools, and those who want to preserve them, will both feel like losers – but neither should. While it still leaves a way for families to buy into privilege, their children would be going to a very different sort of school. It would no longer be possible to buy an ivory tower.

Living in complicated times is tough. It causes us to want to smash, or squash, or overtake. But attempts to crush imagined enemies almost never deliver long-term change. We may want simpler times but, really, we need smarter ones.