Because they are not funded by tax money, their long-term sustainability is dependent on the value they provide relative to the perceived value of a degree from a higher educational institution overall.
Non-profit institutions generally depend in part on academic excellence and creating graduates that succeed in their fields, while for-profit schools are often based on attracting large numbers of students with few requirements in terms of academic qualifications for entry because federal loans are provided for good and bad students alike.
The argument in favor of for-profit universities has been that a student learning from a professor who has never needed to produce their product or service for profit is ill-prepared for a free-enterprise system.
While to some extent proprietary colleges have always existed, their numbers and ubiquitous nature exploded after 1992 when then-committee chairman John Boehner (R-Ohio) of the House of Representatives' Committee on Education and the Workforce killed a federal regulation known as the "90-10 rule", and by simplifying the definition of "institution of higher education" to place for-profit schools on par with nonprofit colleges regarding federal-aid eligibility.
The idea behind the 90-10 rule was that if a proprietary school's offerings were truly valuable—for example, if they filled some niche that traditional state and private non-profit educational institutions did not—then surely 10% of their students would be willing to pay completely out-of-pocket, i.e., those who fell above federal guidelines for receiving taxpayer subsidies to attend college.