There is no reason why public education cannot organise course programmes to cater for these two target groups.

I've already listed the reasons, you just keep ignoring it because you can't think.of a suitable rebuttal.

Most state schools in Europe do not employee native English speakers, instead they rely on local teachers who have gained B2 certification. Once this certification has been gained they will teach Elementary to Intermediate English. But they're under no obligation to continue studying themselves and so it is quite common for LTs to go many years without speaking to an English native. In these cases, going to a private school where qualified native teachers teach up to C2 proficiency level will result in much better, targeted and focused learning of English as a second language.

There is no need for any private "schools" that are not decent schools but just crappy language mills that offer no value at all.

So says the great authority whose only knowledge on the subject of private schools is limited to hearsay and gossip, never having worked in a pirate school himself, and under the very false assumption that all private schools in the world are only out for money. This is simply not true. There is none more ignorant than a person who remains so out of spite.

Most people want to obtain PET, FCE or CAE level English in order to improve their job prospects; these are not exams taught in state schools, so private schools specializing in the CEFR scale are very much needed by many countries.