Peace surely is a good reason, yes. But there are other reasons too.

There are various ways you might define the common good, but that would be one way you could do it.

Ideally a just constitution would be a just procedure arranged to insure a just outcome.

Man is a historical being : The realisations of the powers of human individuals living at any one time takes the cooperation of many generations (or even societies) over a long period of time. By contrast with humankind, every individual animal can and does do what for the most part it might do, or what any other of its kind might or can do that lives at the same time.

A comprehensive doctrine, either religious or secular, aspires to cover all of life. I mean, if it's a religious doctrine, it talks about our relation to God and the universe; it has an ordering of all the virtues, not only political virtues but moral virtues as well, including the virtues of private life, and the rest. Now we may feel philosophically that it doesn't really cover everything, but it aims to cover everything, and a secular doctrine does also.

The principles of justice are chosen behind a veil of ignorance.

Liberal constitutional democracy is supposed to ensure that each citizen is free and equal and protected by basic rights and liberties.