This may be true for almost all university courses, not specifically the MBA. International students' top choice is to immerse in English. The US primarily teaches and lives in English; Europe doesn't.
Some of the factors you mention also count. Private schools have more schaolrship funds. Most top business schools are private in the US and public in Europe. That means there's less money for scholarships in Europe outside of the Erasmus schemes. However, according to the FT's MBA ranking, some of the best value for ROI comes from inexpensive (relative to similarly-ranked US MBAs) European options like Audencia, Cambridge, Cranfield, Durham, EDHEC, EMLyon, ESCP, HSG, SDA Bocconi, TCD, and UCD. There are fewer US schools than European in the top 20 for value.
This may be true for almost all university courses, not specifically the MBA. International students' top choice is to immerse in English. The US primarily teaches and lives in English; Europe doesn't.
Some of the factors you mention also count. Private schools have more schaolrship funds. Most top business schools are private in the US and public in Europe. That means there's less money for scholarships in Europe outside of the Erasmus schemes. However, according to the FT's MBA ranking, some of the best value for ROI comes from inexpensive (relative to similarly-ranked US MBAs) European options like Audencia, Cambridge, Cranfield, Durham, EDHEC, EMLyon, ESCP, HSG, SDA Bocconi, TCD, and UCD. There are fewer US schools than European in the top 20 for value.