That is correct, but it misses the one thing government is essential for. Enforcing the rule of law, which includes property rights.
If you do not have a sufficiently powerful government doing that, you end up with a bunch of warring tribes. Sometime you end up with a bunch of warring tribes and a central government, as in Zimbabwe, or as appears to be developing, South Africa.
You need a government to operate a justice system, property rights, and a way to peacefully adjudicate disputes. That is what the framers set up.
“That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed”
Accordingly:
Governments are instituted to secure rights (whether the danger to those rights is internal or external to those who instituted the government).
Governments instituted to secure rights establish just laws and administer those laws justly. (While “Governments are instituted to secure rights”, I’m not willing to state that all Governments throughout history have been instituted to secure the rights of the governed as well as the rights of those who governed).
And then there are all those disagreements over rights, their extent, limits, and too often their existence.