This has nothing to do with "democracy" in any way. This is the equivalent of a CEO publishing a memo telling employees how to interpret things that happen outside of the company (e.g., new laws, social trends, etc.) It's the CEO's job to align their workforce to have the same interpretation of information. Federal judges can still rule on issues brought before them but the judges have to provide Constitutional- or precedent-related rulings.
Why are Americans acting so surprised that the President has this authority? That is his job, as it was for all presidents before him. This executive order is saying that the "employees under the CEO" do not have the authority to usurp the "CEO's" interpretations of law. Checks and balances still apply, of course; Congress can intervene if the President is acting in ways that Congress doesn't like. That's what impeachment is for--and impeachment is a process regardless of whether the President is issuing "illegal" executive orders or doing something else like what Nixon did.
The process works; blame Congress for not holding the President accountable in the ways outlined by the Constitution.
If you ignore all context, their support of the unitary executive (anti-american) theory, and the recent comments that "if a president does it, it isn't breaking the law" and "going against the will of the president is going against the will of the people"...
If you ignore ALL of that then you have a talking point worth debating.
Because people in independent agencies are by act protected from exactly these things. Think for a bit, why were they not just called "agencies"?
And for all the stupidity of congress, if the fail to protect against a self-coup, that doesn't make it any less likely.
I have a puzzle for you:
Let's say we have a democracy where the only rule is highest vote wins. Let's say 51% of the people vote to enslave/oppress the other 49%.
Maybe they vote for literal chattel slavery. Maybe they vote for healthcare for themselves but not the others. Maybe they vote to tax the others at the maximum possible or implement tax policies that dis-proportionally affect the 49%. Maybe they vote the 49% cannot own homes and therefore must pay rent to a landlord. Maybe they vote that the 49% must register for the draft, but not them. Maybe they vote that the 49% aren't eligible for public school while they are. Maybe they vote that the 49% is not able to own stock or register for a company. Let's pretend those are legal, it is definitely possible. Slavery at one point was constitutionally allowed.
Is that a Democracy? A Liberal Democracy? A Democratic Republic? A Constitutional Democratic Republic if the law were enshrined on paper?
Would you want to live in that country? Would you want to live in that country if you were in the 49%?
What is the key ingredient that makes something a "Democracy" rather than tyranny of the majority, "mob rule," or "might makes right"?