Well, legally, you don't have to monetize the scholarship value simply because it's still considered a fringe benefit, so it's irrelevant to whether they're meeting minimum wage/labor guidelines. I disagree most departments lose money, though. It's an accounting trick.
Say you are a single guy that has a $3,000/mo. salary with $2,800 in expenses. You decide you want more leeway with your budget, so you decide to go get a roommate that's going to pay you $500 a month. Knowing you have this $500 coming in, you decide to trade in your vehicle for a new car that's going to cost $250/mo. extra. Your expenses are now $3,050 a month but your revenue is $3,500 a month. In NCAA accounting terms, you are now losing money. Why? Because the NCAA accounting structure, schools do not count money paid to them from the university's general fund, student fees or government (all considered allocated revenue). Sure, the concept makes sense... it's not generated from athletic activity so it's not counted. The problem? They spend the money on extra salaries for coaches/officials or new facilities, but can turn around and claim it as a loss. Fancy accounting, eh?
The universities don't have the money because they find ways to spend it. They could very easily come up with the money if they wanted to, it just requires budgeting it correctly. The money is certainly there (especially with playoff revenue coming in starting next season and huge television deals now beginning for each major conference).
Essentially, to pay the equivalent of 20,000 full scholarships for FBS schools, it would require an extra $100 million nationwide. That seems like a lot, but it's really not when you consider playoff revenue for football alone will be increasing the BCS deal by over $250 million a year on average. And that doesn't count the future value of TV deals that are going to increase revenues over inflation by a good deal in these next 5-10 years. Paying a stipend for all athletes is a drop in the bucket compared to the money that they'll be bringing in the next decade.