My feeling is that a Raspberry Pi is about the best option you're going to find. This is what it was designed for, after all.
Yes, you need at least a power supply and a flash card to make it work. Those will cost a few dollars extra. You can live without a case for a while if you're careful with it. The mouse and keyboard are generic items that can usually be scrounged up somewhere. Then use a TV for the monitor, just like we did back in the old Atari and Commodore days.
It's true that the Pi is a "some assembly required" system, but at least every system is the same and there are tutorial manuals available. It's way better than getting J. Random Computer from the flea market and then trying to figure out exactly what it is, what works and what doesn't, what OS it can run, etc. -- multiplied by X number of students!
It would be nice to imagine a super-cheap notebook computer. And technically it's doable, but it just doesn't seem to be viable in the marketplace. It would be so limited in functionality that only truly dirt-poor students would want it, which means it wouldn't sell in large volumes, which means the per-unit price would have to go UP due to lack of economies-of-scale, and then the whole purpose is defeated.