The cases that would require more diligence from the insurance company are the kind of research that should be encouraged. Breakthroughs are more likely to happen when people take risks and try something fundamentally new, instead of adhering to the established forms. Your insurance model would discourage such research by making it more expensive.

Additionally, even if we assume that the insurance model is a good idea, it should be tied to individual researchers, not universities. The entire model of university research is based on loose networks of independent professionals nominally employed by various organizations. Universities don't do research, they don't own or control the projects, and they don't have the expertise to evaluate research. They are just teaching / administrative organizations that provide services in exchange for grant overheads.