And of course saying that hierarchies should be mitigated is far from unreal. It was the central message of the people who started America. They put a great deal of effort into checks and balances on power both at the federal level (between the 3 branches) and in having local, state, and federal governments, none of which have a hierarchical relationship. They put a strong emphasis on individual rights, which are counter-hierarchical as well. And let's not forget the freedoms of press and political speech, first among the Bill of Rights, which is very much a check on hierarchy.
I was under the impression that US federal law trumps state law. Is this not the case? And wouldn't that imply a hierarchical relationship?
From this system design, you can deduce that there _does_ exist a hierarchy in the theory of US government — the Constitution is the law of the land and all other actors and subsystems are subordinate to it. Modifying the Constitution requires significant effort at multiple levels of government usually including (by state law) extensive popular support and supermajorities of representatives.
Hierarchy is the rule of men, not of laws. So even if there were a hierarchical relationship between bodies of law, that doesn't require a hierarchical relationship between people.
In the US, federal law can supersede state law, and state law can supersede county and city law. It does have to be written that way of course. In practice, many laws are written to allow jurisdictions to self-regulate within broad limits. For example, in California it's legal to open a marijuana store. But localities get to decide whether it happens in their city. And it's technically illegal federally, but that's currently unenforced.
But the president has no direct authority over governors, and governors have no direct authority over mayors. However much Trump dislikes a variety of San Francisco policies, he cannot just order them changed. Instead he would have to persuade both the House and Senate to pass a law, and San Francisco could challenge that law in the courts.