Yes. Which means it's impossible to use such reports to make general claims about what kind of government is better.
> if a system with a less extensive state that offers less of public services like schooling, infrastructure and health care is what is really better for people, why haven't people made it happen already?
Because "people" can't make it happen in societies where the government controls all those things. Governments have huge advantages over private providers in terms of protecting themselves from competition, without having to actually provide better service.
And even with all those advantages, people still do try to opt out. If government-run schools in the US, for example, were really so great, there wouldn't be so many people trying to get their kids into private schools, or home schooling. But because such people still have to pay taxes to support public schools, those options are only open to the affluent. And schemes like school vouchers to try to level the playing field somewhat never gain any real traction because politicians don't have to answer to the people as a whole, only to special interests--and teachers at government-run schools are a huge special interest.
> gradual steps towards such system should, if they are really an improvement for people, show up as higher scores in happiness surveys.
Only if they exist to be surveyed.