Telemonitoring devices can be used to screen consumers’ characteristics and mitigate information asymmetries that lead to adverse selection in insurance markets. However, some consumers value their privacy and dislike sharing private information with insurers. In the second-best efficient Wilson-Miyazaki-Spence (WMS) framework, we allow for consumers to reveal their risk type for an individual subjective cost and show analytically how this affects insurance market equilibria as well as utilitarian social welfare. Our analysis shows that the choice of information disclosure with respect to revelation of their risk type can substitute deductibles for consumers whose transparency aversion is sufficiently low. This can lead to a Pareto improvement of social welfare and a Pareto superior market allocation. However, if all consumers are offered cross-subsidizing contracts, the introduction of a transparency contract decreases or even eliminates cross-subsidies. Given the prior existence of a cross-subsidizing WMS equilibrium, utility is shifted from individuals who do not reveal their private information to those who choose to reveal. Our analysis provides a theoretical substantiation for the discussion on consumer protection in the context of digitalization. It shows that new technologies bring new ways to challenge cross-subsidization in insurance markets and stresses the negative externalities that digitalization has on consumers who are not willing to take part in this development.