Sounds nice in theory but imposible in reality.
Individual Rights do not conflict with reality. A government that can only maintain itself, and worse yet has the ability to grow, through the violation of individual rights, is a tyrannical machine that operates in direct conflict with reality. It is impossible to perpetuate the existence of such a rights violating machine, it will inevitably collapse into what you will finally recognize as a tyranny.
But that's actual reality... If you're talking political realities, i.e. serious lack of political support for Individual Rights, then it does seem impossible. Collectivism dominates politics, the fact that you're convinced it's impossible for a government to exist without violating rights is some measure of proof.
Membership in a republic is going to come at a cost the only qu3stion is how great.
You seem to think we "give up" rights to form a government... this suggests you do not see government as the source of our rights, so that's a good start.
This leaves two obvious options for the source, but lets consider the source of our Individual Rights as irrelevant for now (unless you actually do think government is the source). Can we at least agree that our unalienable rights do exist?
Next, "All men are created equal" - Every individual is created equal, with certain unalienable rights (that you've hopefully agreed do exist). Each of us is, therefore,
created with unalienable rights equal to those of every single other individual. Are we still in agreement?
Lastly... No individual is created with, and therefore can never acquire, an unalienable right to violate the rights of others.
If we're still in agreement...
My Question to you: How does government acquire the ability to violate the rights of others?
Let me try something different...
Every individual is created with unalienable rights equal to the rights of every other individual.
Governments are instituted to secure our rights as individuals.
Protecting the rights of the individual is the purpose for the existence of government.
Government has no rights of it's own. It is not created with the "right" to violate the rights of others.
Individuals do not "give up" their rights in order to grant government power.
Government power is a unification, not a sacrifice, of our rights as individuals (military/police/courts=self defense).
Government is granted a monopoly on the
legal use of force (to effectively exercise it's purpose for existence).
Governments are instituted by, and entirely comprised of, individuals.
Voting majorities are entirely comprised of individuals.
No individual has the right to violate the rights of others.
No voting majority (which is just a number of individuals) has a right to violate the rights of others.
No government has the "right" to violate to violate individual rights. (and doing so would violate it's purpose for existence)
So, where does that "right" come from?