Medicare should cover children. Then we'd be covering children and the elderly. I think that seems fair--children deserve healthcare (just like education) as a fundamental right. It shouldn't be dependent on their parents.
Be aware that Medicare is a long way from free. At least if you've had a well-paying job in the past few years, Medicare premiums are pretty similar to exchange costs (or COBRA).
Medicare and COBRA are not similar costs. My parents pay half what I would pay if I took COBRA and they have a better plan. Neither of them were struggling before they retired and I'll put it this way, they bought a second home in retirement.