If it is possible to advance your career by publishing uninsured research then we've just renamed the problem, although I do like the idea of adding this structure. Eventually there could be so much of it that it would become an accepted norm that your research isn't actually published in a journal until five years after you informally publish it. Other scientists in the field have to be abreast of the latest findings, so now these informal publications are the true journals.
I see your point, the success of this would have to align with a change in the broader academia to only cite research from insured researchers.
The "organic" way this would happen is if there was a shift so that journals with insured research are far more valuable than uninsured research. Or perhaps if companies started suing researchers for negligence and fraud and recuperate costs if they used research that was later proved to be fraud.
In the literary world, anyone can publish a book, but a book from o'reilly caries with it a different level of authority and diligence then a self published book or blog post.
So the shift would have to be that your career can't advance without publishing a bonded and insured paper.
But that is not how research works in Academia. They have to follow the bleeding edge of the field, or they may be doing work of their own that is already irrelevant. They will not wait until a consortium of insurance companies and underwriters have done the actuarial analysis and come up with an underwriting product that the institution has funded (and what is the institution's business model for recovering this cost in a field of pure research, anyway?)