Why students protesting tuition hikes in California are well-intentioned, but misguided

From CNN.com:

Students were occupying buildings Friday on several campuses of the University of California system in protest of a 32 percent tuition hike.

...

University officials said the $505 million to be raised by the tuition increases is needed to prevent even deeper cuts than those already made because of California's persistent financial crisis.

Protesting students said the hike will hurt working and middle-class students who benefit from state-funded education.

While well-intentioned, the students are failing to recognize the simple economics of education.  Students demand education--therefore there is a demand curve for education(click the diagram to the right)  that is downward sloping: some are willing and able to pay more than others.  Private educators are willing to supply education, but it is costly (Private Tuition).   For a variety of reasons--affordable access to education, reduced crime, increased productivity--society, through state and federal tax revenues is willing to subsidize education thereby reducing the costs of education (S_public).  This downward shift in the supply of education decreases tuition (Public Tuition) and increases the number of people willing and able to get an education.

So what happens when the state reduces the subsidy, as California is currently doing? Starting from the fully subsidized situation (S_public ), the reduced subsidy will shift the supply curve back to the left raising the market clearing price of education (Current Tuition + hike) and reducing the number of number of people receiving an education from Q_before to Q_+hike.  Not only are fewer people educated, but those losing access to education are those with the lowest willingness to pay OR ability to pay.  And this is where the protests come in.  The increased tuition reduces education among those with the lowest ability to pay.  Sounds protest-worthy, right?

But, what happens if tuition isn't raised in the face of the reduced subsidy?  In that case, the price of education would stay at the current Public Tuition level in the diagram, but the supply curve still shifts left (actually up) by the amount of the reduced subsidy.  If tuition doesn't rise, the quantity of education supplied at the current tuition would be less than if tuition rises (Q_nohike in the diagram). 

Contrary to the tuition hike case, it would then be a crap shoot as to which students lose out on education, but the end result in unambiguous: a successful protest for no tuition hikes (assuming state funding for education is cut) will result in less total education than allowing tuition to rise. 

 Is that really what the protesters have in mind?