The constitution is just a bunch of laws and it is the law of the land. It is possible for the constitution to say "All citizens must stop drinking" and for it to be enforced just like any other law but it also establishes laws for the federal and state governments as well and it is supreme to them as well. This makes it something that can be used against the government and that same government can use it against the citizens. This means that we are all on equal footing with respect to the constitution and that is that we are all subject to it no matter if we are citizen, state, or federal government.
I think the founders were quite brilliant in establishing it as the law of the land because if I have to obey the laws the constitution establishes for me in it then so does the government itself which makes the government my equal no matter if it is local, state, or federal.
There are several reasons why the Founders had to include the Supremacy Clause. The main being that without it a Federal Republic would never work, there has to be a final arbiter and a measure of uniformity throughout the States or all you have is what they were getting away from: a Confederacy. That worked out so well they scrapped it and started all over again! You can't have fifty people who all want to go to a different part of the park walking one dog, the poor dog will end up torn to pieces every time.
I will say the only attempt to use the Constitution as a "Thou shalt not" against the citizens was the unmitigated disaster that was Prohibition, and I doubt the States would be dumb enough to try it again. (I hope, anyway)
OK but the only difference I have is that the constitution and all laws in congruence with it are the supreme law of the land. Its not the federal government, any state government, or any citizen but it is the constitution itself that is. This makes us all subject to its written authority.
Other laws come and go, the Constitution itself is the only supreme law of the land. It's at the top of the pyramid called the hierarchy of law. Don't make the common mistake of confusing statutory constructs with constitutional authority. The rest of the laws created in accordance with it fall in layers beneath it, but only the COTUS itself is supreme.