Is the for-profit model feasible to higher education institutions? In other words, are there any for-profit schools that have achieved a good reputation in academia (teaching and/or research)?
This answer is about the US.
Are there any for-profit schools that have achieved a good reputation in academia?
As far as I can tell, the answer is (1) we don't know, but (2) probably not.
The reason it's difficult to know the answer to this question is that although there is a variety of mechanisms for judging the quality of education at non-profit schools, such mechanisms either don't exist or aren't working well in the for-profit sector. US News and World Report doesn't rank for-profit schools. There are accrediting bodies, but the ones that handle accreditation for for-profit schools seem to be lap dogs of the industry.
Because of the lack of data, people in the federal government who have been trying to crack down on fraud have been forced to use various proxies as measures of educational quality. For example, they look at the percentage of graduates who default on the government-sponsored loans that they used to go to for-profit colleges. People have also tried to figure out what percentage of students at these schools actually end up employed in their field of study. All of these statistics are at best indirect measures of quality, for-profit colleges tend to come out very low on these measures, and the colleges tend to give out fraudulent numbers to try to make themselves look good by these measures.
You can try to try to pick out a specific college, or a certain program at a certain college, as a success story. I didn't have much luck at that when I googled. One article mentioned Microsoft certifications as an example of something reasonable that you could pay a for-profit college to help you prepare for. But when I started looking up information on Microsoft certifications, it basically sounded like a scam in which the instructors are really not vetted at all, and the purpose of the program is to achieve sales and vendor lock-in.
Another example I've heard about is that often community colleges don't have enough capacity to handle the demand for certain programs like nursing. In theory, it would seem to make sense for the private sector to take up the slack. As private, non-union businesses, they are more agile. But the reality seems to be that these programs are of extremely low quality. For example, stories abound of students taking a semester-long nursing course in which five or six different instructors come and go before the course is over.