The idea of ‘workers controlling the factory’ is indeed ‘democratic’. That doesn’t mean it’s the best way to function. The United States is not a Democracy its a Constitutional Republic.
Actually, it isn't. Don't know what your background is, but if you ever saw a communist country in action, you wouldn't likely to say that.
The "workers" never actually do "control the factory", the Party & the government does. The Party & government tells it what to produce, how much to produce, controls the access to raw materials, the staff, the output and the distribution of the goods. The "worker" is just a replaceable cog in the wheel, not "a free person". Real democracy requires that there be "free people ("demos") in order to have "democracy".
However, your point about the US being a Constitutional Republic is true.