Et tu Blood?   
 
 
Your 1st assumption is painfully wrong.
Healthcare for everyone is definitely not free.
Your tax base must cover all the governments's whims, including your so-called right to free health care.
Not to mention the unintended consequences of such a system wreaking havoc on the morals of humanity.
What is the cost of a life again in a pluralist pool?
Meaning, you really want grandpa or grandma to get that brain tumor removed so he/she can attend a grandchild's wedding, but socialized medicine accounting rule #673 cuts off this procedure due to poor return on investment.
Solution: Take a medical tourist trip to a for-profit medical facility that greedily wants your money, not your love or devotion.
And grandma/grandpa has to pay for this with their own money even after contributing to the national health pool in taxes.
Exactly because you have a guarantee of health care, countless thousands of wasteful medical visits choke your physicians and clinics with mundane queues, when, if push came to shove, and everyone felt a sting in their wallet, would-be patients would think twice before strolling to the doctor for a headache or flu-like symptoms.
Better you champion the last bastion of freedom over here than ride the slippery slope of chronyism, marginalized medical procedures, and accounting decisions on what life costs? Over here, life costs dearly, so dear, please mind your costs.
What you mistake for coldness is resistance to forced redistribution of hard earned money to ungrateful recipients.
Charity on the other hand, is what you seek. 
Removing the middle man(government), I can direct my money at my choosing to those truly deserving.
In the end, health care is only one of many commodities that are flitted about as a lure to your spending dollar.
Medicine is no different than a playstation or a motor boat or a vacation home.
All nice things to have, but each citizen must decide which they can afford and cannot.
LOL, you prefer these decisions made by an unloving, disconnected government?
How long before they rule a 2nd childbirth too expensive?  

The nice thing about standards is there are so many to choose from. ~ Andrew Tanenbaum