No, absolutely not. One step closer to New World Order. I know that's a bit dramatic but i believe that would be a bad idea if for no other reason than the fact that we all have different social, cultural, socioeconomic, historical, etc backgrounds that form our traditions, laws and norms.
There's already the Hague for crimes against humanity so protection would not be something the global constitution would need to cover. We already have international trade law.
It would make sense if we ever found life on another planet but as of now, autonomous states settling through the UN, Hague, etc are more than enough. While you may point out that those *(as well as many other international institutions) are highly flawed, can you imagine the turmoil from trying to get 196 countries to agree on an exclamatory document. I'd rather not go there.