How does this explain why full tuition should be paid?
If they pay just the teachers and nothing else, they should be able to issue a discount.
This is not necessarily the case. I do not have numbers, but there are definitely some important counterpoints to this. (not in any specific order)
1. Mortgages and many other fixed expenses continue to be due.
2. While during the original 2 weeks before pesach many schools used free teleschooling options, those options were not really viable and had many shortcomings which caused many schools to move to more complex and costly systems.
3. Many utility bills will have gone down but not disappear and some may be billed at 75% or more of the original cost for various reasons which I will not get into here. (This is my business expertise-just trust me on this one)
4. There have been equipment and printing costs which they would not have had otherwise
5. Many schools help support the school by having a simcha hall or the like which may have dried up. If now this major source of income is lost, at least they can cancel it out with some of their savings (if they have any)
6. Some items which you are assuming that they are saving may be subsidized by the government or other funding. An example is the lunch program. Many schools receive government funding to cover lunches. They do not save anything by not providing them-just the opposite. They may be losing money on the deal.
7. Other regular fundraising avenues may have also dried up. Many mosdos have their fundraising dinner during sefirah when the halls can give them a discount since they would not be making weddings anyhow. The inability to make these fundraisers can be a very big hit to their budget.
8. I am sure that there are many whose tuition payments have stopped cold turkey. Some due to the inability to pay due to the current financial situation and some because of the attitudes displayed in this thread.
I am sure there are more points in both directions, but your premise is definitely not simple.