Even in such countries one could rely on a car. Some medical things aren't covered fully or require prepayment to be reimbursed later ( e.g. dental or glasses,

Even in such countries one could rely on a car. Some medical things aren't covered fully or require prepayment to be reimbursed later ( e.g. dental or glasses, but we're talking a couple od hundred euros max, not tens of thousands). There's also natural disasters or unexpected maintenance, appliances dying, roof/plumbing leaking, etc. In general though, i think for most EU countries a few thousand euros is enough of an emergency fund, depending on circumstances of course.