Hundreds of thousands of drivers who pick up passengers for Uber Technologies Inc. and Lyft Inc. are frustrating a push by big insurers to sell new ride-sharing plans. Firms including Allstate Corp. and Geico are eager to sell the plans, which are more specialized and typically more expensive than traditional auto policies.

But many motorists are unsure about the extent of their current coverage, confused about their options or unwilling to pay beyond what is legally required, according to insurance executives, analysts and drivers. Ride-sharing drivers aren’t legally obligated to pay for anything beyond personal auto insurance.