The most important asset for a private school is connections.
I've experienced schools that were directly tied to the industry, so that the local companies would first go there and check with the teachers to see what student would be suitable for their company, instead of advertising the position through the usual channels.
The student would go from graduation right into employment without having to do any actual job search.
If you are an institution that has an established connection to the local industry, then I think such a school would be able to survive the online offerings from other international schools/sites.
I'm not sure how that "wealthy families" part fits in with this?
Maybe this depends on the country, but one example that relates to my original comment was a school which specialized in university students who are about to or just finished their studies and wanted to enhance their studies in a specific area.
The whole program was less than a year and the costs would be easily covered even by a few months of part-time work, so we're not talking having to get an actual loan to even attend.
I've experienced schools that were directly tied to the industry, so that the local companies would first go there and check with the teachers to see what student would be suitable for their company, instead of advertising the position through the usual channels.
The student would go from graduation right into employment without having to do any actual job search.
If you are an institution that has an established connection to the local industry, then I think such a school would be able to survive the online offerings from other international schools/sites.