Some might but many wouldn't though, because the risk of a problem occurring is still relatively low. No insurance just means it's worse if it does happen. The company would fail, resulting in a loss of service for their customers and a loss of jobs for all the staff.

To use a good old car analogy, if car insurance stopped paying out people wouldn't all immediately become better drivers.

Production reliability and user privacy are different goals. It’s true that a generally tighter ship will be better at both, but they are often in direct conflict. “Fail secure” is an outage waiting to happen.