The relevant factor here is surely not 'private individuals', but 'private individuals with more than £35000 in a single bank'; there are at least three banks and most people with more than 35k in savings are reasonably risk-averse and financially competent, so you're dealing (in the context of a crisis caused by peoples' increased propensity to refrain from saving and live off credit - mortgage withdrawal rates only went negative this quarter, net saving is now tiny-but-positive rather than actually negative) with the relatively small set of people with more than £100k in savings in a bank.

I suppose there is a 'but what if Abbey go bust during the two-hour period that my house deposit is passing through them' worry, but insuring sums deposited for less than 7 days would handle that case.

You're creating a strong incentive to sell shares in anything that looks remotely risky and put the money into Halifax six-month bonds paying 7%, which is nice for Halifax until April but seems somehow sub-optimal for every other public company.