That is exactly what will happen if QI goes away, and taxpayers will ultimately pay the premiums. Maybe that would be better, or maybe not. But in general, few policemen could withstand the risk of a single ruinous suit, and without insurance of some kind, would be forced to flee the occupation.
The problem is that the legal system has a quite noticeable element of randomness to it. Despite what you may have read, justice is not always done. (source: have been on the receiving end of this)
As a practical matter, if there is possible liability, everyone will have to have liability insurance, just as in the medical professions, for example.
