Hood is talking not for the here and now, but for 20 years plus down the line. If they could, I don't see why not- it'd free up more money for everyone else. In reality, only Oxbridge have the might to raise that sort of cash from endowments- while a few others could get away with charging higher fees, they simply don't have the donator network to sustain a large endowment fund in order to shake off state funding. Most private (and some state) universities in America have at least several billion dollars of an endowment to invest, by contrast, outside of Oxford and Cambridge's combined £9 billion (still half of Harvard's figure), only five other UK universities break the £100m mark- Edinburgh, Manchester, Glasgow, UCL and KCL. They'd all need to quadruple that figure plus make significant returns on how they invest it to even think of reducing their dependency on the state.
It's debateable the effect this will have on students. Arguably, standards will slip based on those who can afford to pay. But the much larger scholarships could attract some very talented students that might be financially better off applying to Oxbridge, and perhaps redressing the balance (I don't see Oxford doing it but Cambridge not). In addition, the better funding available for the rest of the Russell/1994 group etc might see them improving relative to other countries aswell, making it perhaps a win-win situation. At any rate, this won't happen any time soon, so I suppose the point is moot for at least the next VC's term.