There is nothing legally wrong in the idea, though some posters have jumped on their moral high horse. Ryanair for example have adopted a surcharge for this EU261 risk and as a result I would have no qualms arbitraging these guys. Whether I would do it with BA is a different story.
The problems arise more from practicalities as highlighted - there is a risk the delay was not caused by the airline and would not give rise to compensation payment, and there is the issue of the cash float needed while waiting for the repayment.
As a result I think the idea is more suitable to flexible young professionals who are willing to risk that their last minute trip to London is not partly funded by the airline - rather than students who need the cash upfront.
I have never tried this and never thought of it before in all honesty, but given the number of followers on this forum there must be someone who has done it. Thanks for the idea though.