Potentially yes. But those colleges won't have the prestige and long history that a college needs to serve as some kind of credential, neither will the inherent network-building happen there either. What I mean is that because Harvard is such an elite school, many of the people you meet there WILL be involved in society at the highest levels and you'll already know them. That gives you a powerful advantage. University of Phoenix doesn't have that yet and may not for several decades. And the University of Phoenix doesn't carry much prestige or brand recognition with it.
Furthermore the job market doesn't necessarily support the need for additional college grads. In a "normally functioning" (total bullshit I know but go with it for a second) job market high wages and high employment does two things:
1. Increases people's ability to pay for loans post-graduation
2. Reduces the average default risk
When that happens, interest rates for college loans go down and more people are able to go to college based on fundamentals: the job market will (with some lag factor) still be good when they graduate and thus loaning to them is a good idea. This is a "natural market function" which, though imperfect, tends to balance out the supply of college with ability to demand. I would estimate that college loans would tend to lag the job market by somewhere between 2 and 10 years depending on how agile a bank was to react to the job market. So you would have a period of heightened wages for at least 4 years as people worked their way through school and then potentially a period of lowered wages for a few years as people slowly figure out that the crazy high wages are gone.
But with these subsidies you get all the downside of the glut with none of the upside of the scarcity. It's not awesome.