No matter what your criticisms of the US may be, it’s indisputable that there are a lot of places in the world that are objectively far worse.
That said, “If someone is unhappy in the US, they should just leave” is a bad attitude to have IMHO. If someone is unhappy in the US, they should figure out why they’re unhappy and advocate for positive change. Don’t run away from the problem, be part of the solution. “Take it or leave it” is not what a democracy is supposed to be about.
This is true. It is not possible to “overstay” or otherwise violate immigration restrictions in a country where you’re a citizen, because those rules do not apply to citizens.
That said, this can still cause you trouble. For example, if you enter the country on a foreign passport, your name will typically be entered in a database of visitors and whatever departure date they give you will also be entered in that database. This is incorrect as you’re a citizen, but if you give them a foreign passport, how will they know?
Once that departure date hits and no departure is registered under that name and passport number, it’ll be flagged as an overstay. Which can lead to consequences such as being stopped on departure when you DO try to leave (from a country that has exit controls) or having to manually correct the database if they encounter you in some other context (say, traffic sobriety checkpoint, to pick a random example.)
These logistical problems tend to be worse in countries that don’t have a central registry of citizens and/or residents, and avoiding these kinds of scenarios is why it’s best to enter and depart countries of which you’re a citizen on that country’s passport. And why you want to use the same passport on arrival and departure in each country you enter.