There are the same number of mentally unwell people. Mental illness typically follows normal distributions sans PTSD in war torn countries. The difference is the approach. Most European countries use a carrot
and stick approach. There are no laws guaranteeing the homeless the right to live on the sidewalk, as there is in California. They can be fined or arrested here in Denmark for doing that. Ditto for begging. So they don’t congregate in large numbers in cities and there are no tents. Further, drug possession and distribution is prosecuted. The penalties are scary enough for the hard drugs to discourage broad use.
That’s the stick. The carrot is a generous welfare system which isn’t afraid of invasive intervention. Those deemed a danger to others or themselves can be detained for treatment. Involuntary commitment has virtually disappeared in many US states. Mental health treatment is also free, so there isn’t a barrier to access (though lately it has become harder to access treatment which isn’t considered acute).