The government can never increase freedom. It can only reduce freedom.
The only way to increase freedom is by reducing the government.
If I have universal healthcare, then I am free of the worry of medical bankruptcy. Being free from things is a significant source of freedom.
Also, quite a lot of treatments are not done, or have absurd waiting lists, so you’ll be tempted to get yourself into medical bankruptcy anyway by going private/abroad. Either that or accept delayed subpar care. Or no care at all.
freedom is not the opportunity of doing whatever you want without any limit, if they leave me in the desert and tell me "you are free now, do whatever you like" I would not be free at all.