When it does work is when insurance has no influence on the price of goods, and is a minor consumer. For example, when fire insurance pays to replace your goods that burnt up.

When it doesnt work is when insurance is the predominant purchaser of those goods. A good example would be US health insurance, which has an 80/20 rule just like your proposal. Health insurers by law (ACA) must pay out 80%, with 20% allowed for opex and shareholder returns. The Hazard is that as an industry, to increase returns, you want the cost of care as high as possible, thereby maximizing your allowable profit.

It is a similar problem to how power is regulated in California, which has a mandated profit cap as a percent of costs. As a result, these regulated companies have the highest opex and cost of power in the nation of approximately $0.50/kwh