This is exactly the criticism that would be leveled by classical economics. However, that would be ignoring the fact that there's essentially no such thing as a free market when it comes to producing *most* goods - especially goods whose demand is inelastic - so the goods we already consume are already of an inferior quality relative to the goods sprinkled with magical pixie dust which the free market could ostensibly provide. However, widespread discontent with government run services either because of their inferiority or delays in receipt, could cause social discontent, which in a democracy would mean loss of power for the people generally in-charge of the government, and potentially privatization efforts (loss of employment, potentially for the bureaucrats who run the entity) for the state apparatus. It could likewise make the populace more willing to contribute additional funds or cut other programs to finance well-liked programs.
Your last question on timely manner is another question that deals primarily with the question of "equilibrium" economics. That is to say that in a standard supply and demand model there's a point at which the lines cross and create "equilibrium" that means you're providing and producing goods at the optimal level for revenue. If you were to impose some other sort of regulation (monopoly, trust, price floors, monopsony or price ceilings) the argument can then be made that you bring the market out of equilibrium and force a glut or shortage, with additional modifiers from the relative elasticity of demand. In educational matters this particular factor is really played up in the media, for example how prized test scores are in Vietnam and China, because their free in-country tuition forces students to seek out the very best grades and test scores or they won't be given the opportunity to attend the more desirable universities - intrinsically this is meant to say there's a shortage of universities with desirable qualities. You also see it in healthcare with ridiculous anecdotes about waiting for healthcare in Canada, etc.
I'll even draw a shitty graph:
http://i61.tinypic.com/2076l48.jpg
(I should note that you could also tell how much the program would cost by taking the area of the triangle formed by ceiling-supply, ceiling demand, and post-ceiling desired-supply, and doing a little calculus - so if you wanted to fund the program in advance (as most governments do) you could also find what your actual supply would be in the event that you had no intention of providing the post-ceiling desired supply)
The state has three options in the case of a shortage: raise prices, expand the supply, or let the shortage continue (planned privation/rationing etc). In the case of university being provided free to the user, you'd have only the latter two options.
In short, ideally a highly elastic good in a free market will see users switch to a different supplier if they don't like the commodity they receive. However, in a state context, instead of just switching suppliers (which may yet be possible in the form of competing private institutions or leaving the country) one could also exert pressure on the state itself through the vote, or civil disobedience. Either would work.