Travis, I think you make some excellent points, here. These are indeed public property in this case, and they could still be very useful for at-home use for low-income folks (especially for young kids doing math practice and such, as you say).
The problem, I think, is the cost of distribution, setup, and support. To set up an office and/or use staff time to figure out who's eligible, to do all the communication and outreach, to bring the computers to homes and make sure they're up and running, to install the relevant software, and to do even minimal tech support - that would be a major expense. If the town or school district were able to raise or allocate enough money for all that, then they would probably wish to do so for computers that were a bit more current - i.e. capable of going on the internet. If you were talking about, say, 200 computers, they could probably bulk-purchase a bunch of internet capable Linux machines for less than $80,000 - still a lot of money, but in another sense probably far less than the combined other costs of such a program (staff, transportation, etc.).
Now, it would be great if they could instead donate the computers to nonprofits like yours - which are already set up to weed out the busted units, refurbish the good ones, and deliver them one by one to needy homes.
M