Shell Management;
The structure you suggest is what all airlines should have but too many Directors of Ops fear being made to look bad rather than welcoming the benefit. It is also the way to foster open rather than confidential reporting.
Having the Flight Safety Department controlled by and reporting to the VP of Flight Operations only works if the Flight Operations VP and his/her organization wants to know about flight safety issues. At present, they seem satisfied with the operation, we haven't had any accidents and therefore have no need for a flight safety program that may impede commercial priorities.
We collect all kinds of FOQA data but do nothing with it - nothing that is effective anyway. We even have to wrangle an invitation to training and standards meetings because we're often "forgotten".
I can tell you from personal experience that getting a FOQA Program going without the support and buy-in of Flt Operations or the CEO, (even getting the CEO's awareness, let alone buy-in, is a significant problem here) is simply a complete waste of time, human and technical resources and the organization's money. We have been beating our heads against the office refrigerator for ten years and it's a lost cause.
So, no, I don't think that "reporting to Flt Ops" is a good idea if they don't want to know. I think the CEO needs to know how close his/her airline came to an accident, (we can show at least a dozen "events") so he can comprehend the notion that the airline business is about more than marketing. Then, just maybe, he might kick some ass down below and get his people onside because right now it doesn't "hurt" for people to ignore the data.
If there is a healthy, knowing safety culture which has an appropriate level of intervention as per previous discussion and a good agreement with the association, (and we have an excellent one that is respected by both sides) where flight safety has both independance from operations and the ability, with teeth, to intervene where the data indicates, (I fully realize the problems in this requirement but expect that a healthy safety culture is one that doesn't ground every 767 no matter where it is around the world with a 5kt flap overspeed!, etc, etc), then a working relationship with Flt Ops which respects and asserts the requirements of both departments so that commercial and safety interests are intelligently balanced through the use of data and not just opinion or politics, can work effectively for the organization.
Anyway, enough. I guess we're going to learn the hard way.