Rights try to predefine 'best possible' for a culture.
This is a good thing because it provides a written moral standard and a legal basis for further argument - rather like a constitution.
Relying on 'rational argument' doesn't work as well because most 'rational argument' in politics, law, and economics is persuasion through sophistry, custom, tribalism, rhetoric, appeal to self-interest, and/or the application or threat of force.
None of these have much to do with rationality in the scientific sense of being able to build useful models of reality from data.
tl dr; Defining rights makes spurious political plays more difficult.
Rights approximate the structure of laws that people agree in some vague way should exist. My point is that any discussion about rights can be reframed without ever using the word 'rights' and usually it is much clearer and more consistent to do so.
Most of the time you can just say something like "It should be unlawful to do X in situation Y because it undermines the ability of those involved to make predictably good decisions."
Rights are useful in the same way that asserting "pi = 3" is useful: it's simply better than nothing. It is hardly some kind of ideal, despite how easy life would be if it were true.
They may be ultimately arbitrary, but until you come up with a final conclusive objective ethics, proven metaphysically beyond questioning, the rest of us have to make actual decisions today. The UN, as a collective body, defines various normative concepts, e.g., by defining "human rights." If you have issues with them, you join the proverbial mailing list and state your case.
This is a good thing because it provides a written moral standard and a legal basis for further argument - rather like a constitution.
Relying on 'rational argument' doesn't work as well because most 'rational argument' in politics, law, and economics is persuasion through sophistry, custom, tribalism, rhetoric, appeal to self-interest, and/or the application or threat of force.
None of these have much to do with rationality in the scientific sense of being able to build useful models of reality from data.
tl dr; Defining rights makes spurious political plays more difficult.