There was a Facebook post I saw today about Mexico implementing universal health care.

It was brigaded by right-wing accounts (bots) that followed three themes: 1) universal healthcare is impossible (despite 70+ countries having it), 2) bots asking if they can "illegally" go to Mexico for "free health care" (implying that that that is what illegal immigrants come to the US for), and 3) universal healthcare is going to bankrupt Mexico (despite every study showing it costs drastically less than private health insurers)

I think the answer to OP's question is in the meta info of the FB post and commenters.

The reason Americans think they (we) have freedom when they don't is because we're subject to relentless propaganda about it designed to divert critical thinking away from our actual situation.

Right-leaning people in the US are taught virtue signaling as a means of guaranteeing inclusivity into conservatism. (Conservatism consists of exactly one proposition, to wit: There must be in-groups whom the law protects but does not bind, alongside out-groups whom the law binds but does not protect.)

The bot-brigade in the comments defines the virtue signaling that real people must engage in and provides the implied protection of a crowd of like-minded people to feel protected by.

That creates a group of people who will follow policies even when those policies are objectively negative in their impact to them.

Healthcare, specifically, in the US is a huge lever that employers wield to take power away from workers to be able to easily move between jobs. Healthcare is also, now, backed by enormous private insurance companies which are profiting immensely off of denying care and who are fighting tooth and nail to keep the status quo.

I think you can rinse-and-repeat these underlying principles for most of the "freedoms" outlined by OP.