Reputation would follow the institutions, and graduating from an institution that set lows standards wouldn't have any signalling power to prospective employers, so students wouldn't want to enroll there.
What you actually see in countries that have both a private and public education system is that the private institutions compete on the grounds of who sets the highest standards, not on who offers the most riskless opportunity to students to get the degree, irrespective of how low an effort they put in or how incapable they are.
If you're talking of a huge number of small institutions in combination with high mobility, then maybe reputation at the level of the individual institution wouldn't do the trick, but you would probably see certification and quality assurance agencies pop up to establish brands and enforce standards around them.