Don't agree. If access is free then a lot of preventative care can be done in order to not have to conduct expensive critical and emergency procedures.
People in this country don't go to the doctor because they may or may not end up owing sums of money ranging from $0 to many hundreds of thousands, depending on the combination of provider, doctor, insurance policy, state and federal laws. So people just stay away. Until they have a heart attack, or cancer is in the terminal stages then they are rushed to emergency and then guess what happens -- a very expensive procedure probably needs to be perfomed. So not very surprising that health care is expensive.
But let's take from another point of view. You say it is expensive. But how come Scandinavian and many European countries manage do provide it? Could it be that we just spend everything on defense (well...I personally called it offense but let's keep it official here) -- more than all the countries in the world combined? Do our doctors and medical supplies companies charge insane prices? I don't know the answer, but I know it has been done in other countries, and it is currently better than here. So it seems like it is possible.