This is how I got my first computers; obsolete and broken computers cast off by people wealthier than I was. [1] It's great, because you get to learn how to fix the computer as well as whatever it is you learn on the computer. I imagine my life experience is super different from those you are helping, but I can tell you that early experience fixing obsolete computers has vastly helped my career.
It is a lot more labor intensive, because you have to have someone to teach the kids how to fix the damn things, (for me, my dad and a copy of minasi's "upgrading and repairing PCs") but once you have that skillset locally? it's probably sustainable, because the rich will always be throwing out last years gadgets.
In some ways it will be way easier for you than for me; when I grew up in the '80s and '90s, there wasn't a lot of standardization, so with my 'catch as catch can' hardware acquisition strategy, I'd have to completely change my software stack every time I got new hardware. These days? Most educational software runs in a browser (I use and heartily endorse Khan Academy for the parts of learning that can't be done from a book alone) and so you can have a diverse fleet of hardware and even operating systems, and as long as you have enough local skill to bring the things up to the point where they can run a browser, you should be good to go.
The big problem with this plan is power; Nicer gear from the aughts ought to run a browser just fine, but it will chew up a lot more power. If you have to pay for unsubsidized electricity, more modern gear might make more sense.
[1]There was also this really juicy (for me) sense of acquiring "means of production" - I owned these computers that others had cast off as worthless or broken, and I turned them into a useful resource for myself. I think that if you could work something out so that the kid in question gets to keep the computer they fix... that might be extra gratifying. I know it was for me.