The thing with employer-led insurance schemes, you then end up with a system similar to American health insurance.
It gives employers more power over the lives of their employees (and families) which a few would no doubt use unscrupulously. If you know that getting fired or made redundant means that your disabled child would go without insurance support you are likely to change your behaviour in a way that benefits the employer, but is detrimental to yourself.
Do we really want to start to move towards the US model of competitive over-working? DH works for a "liberal" US tech company. Despite being more progressive, it is still expected that you will refuse to take all of your annual leave, work 10 hour days minimum and work over weekends / nights as required.
It's fine for a short while when you're young to build a career or to reap decent wages. But long-term it'd put you in an early grave. Which any parent would do, if they thought their child needed access to some critical illness insurance.