The subtext being that homeschooled children grow up into worse citizens than schooled children? What is the basis for that?
Another reason is that if you're not participating in common institutions you have no stake in them. If everyone goes to the same schools (in Germany the idea of the Volksschule), everyone has to participate in civic discourse about what to teach, how to fund education, and how to maintain equal standards. There is a common fabric and shared reality because everyone shares the same space.
That's obviously not to say that literally every homeschooled person is disinterested in public life, or vice versa but I think it's hard to see many other motivations for homeschooling other than to withdraw for one reason or another.
In the US, secularists have made a concerted effort to scrub every trace of religion out of public life and impose French-style secularism on a country that’s as religious as Poland. And they did that not in the 21st century, but in the 1960s and 1970s, when both Germany and the United States were vastly more religious.
Folks who want to homeschool their kids for religious reasons aren’t the nuts that American media makes them out to be. They’re people who in Germany or Sweden or the Netherlands or many other places would be able to avail themselves of public options that those countries include in the mainstream.
[1] Germany appears much more content to let social mores evolve organically rather than tearing up the social fabric by rushing change. Germany is a much more liberal country than America, but the laws are much more conservative in many ways. A subset of Americans are besides themselves because the Supreme Court overturned a case recognizing a right to abortion until viability (22 weeks). Meanwhile, Schwangerschaftsabbruch I (deeming abortion to be a violation of the Basic Law’s right to life) is still the law in Germany, and decriminalized abortion is permissible only to 12 weeks. Nobody called Angela Merkel a fascist for voting against same sex marriage. Bavaria requires crosses in public buildings and hasn’t been kicked out of the country. Etc.
(It doesn't work out great for Birmingham!)
Crucially, South Asian people are endogamous, meaning that they generally prefer to marry within their communities and moreover within the family: cousin marriage is common. So there has been consistent secondary immigration from the subcontinent as South Asians marry spouses from their communities from their countries of origin and bring them to the UK.
The average Bangladeshi or Pakistani citizen's religious views are about as welcome in Britain as the average Briton's secular views would be welcome in Bangladesh. Which is to say that they are disjoint and cannot be reconciled much at all.
What's wrong with disassociation as a motivation? In a borderless world I don't see a reason for forced participation in a place that one might not even like. So long as everyone pay their financial debts, how they live their life shouldn't be anyone's business.
As if that happens in American public schools lol.
More seriously the Prussian system was created after the Napoleonic Wars to ensure that Prussia had a large reasonably well educated population suitable for warfare and for industry.
That system was enforced in the USA later in the 19th Century.