Theoretically yes, practically no. If coverage is universal and mandatory, companies will invent all sorts of ways to market themselves to a low-risk subset of

Theoretically yes, practically no. If coverage is universal and mandatory, companies will invent all sorts of ways to market themselves to a low-risk subset of clients -- car insurers marketing themselves as women's insurers, health insurers advertising their online capabilities to attract younger clientele. The clean way to do it is to separate insurance (can be very efficient if privately provided) from redistribution (will lead to bad distortion unless done by the state).