On the question of whether indemnity/ insurance costs might have a greater impact than any regulation changes, I think that there is reason to think that this is unlikely.
Insurance underwriters are fairly dispassionate and analytical as a breed, and of necessity look through the human aspects of accidents to the financial. Courtesy of the 1700 or so deaths on UK roads each year, not to mention a much larger number of injuries, there is a substantial body of case law, not to mention custom and practice which enables underwriters to assess the likely financial impact of loss of life and serious injury resulting from an accident involving one of their insured. In arriving at their premium rates, insurers use sophisticated risk assessment and management techniques, and I believe that dramatic premium increases for all insured tend only to arise where something transpires which changes the risk landscape fundamentally.
In this case despite the horror of what has happened, I do not believe that the outcome has a significant impact in underwriting terms: the possibility of an insured aircraft having an accident and giving rise to third party claims will have been one of the risks understood when premium rates were established. Whilst the loss of so much human life has shocked us all, the eventual cost of the accident to the underwriters may well not fall outwith their estimates for a such an eventuality, bearing in mind they will have had to consider hypothetical scenarios such as a FJ crashing into, say, a shopping mall, etc etc.
In considering future underwriting rates, they will focus on whether the risks have gone up, down, or stayed the same. Even if there are no regulation changes (unlikely I think) all operators and pilots will, at least for a time, become more conservative, with the result that the prospects for a similar event reduce, and hence the risk insured goes down.
All rather dispassionate, and not intended to suggest that on a human level, underwriters would be any less shocked than the rest of us.