If only all the people in a given country were united under some common organization that could negotiate on their behalf....

Negotiate with who ? They set the rules

Coordinating activities is different from happening to act the same way.

the act of uniting is literally antithetical to being independent. I can't even understand why you would ask that question. Why can't red be blue, makes about as much sense as asking why independent people couldn't unite and still be independent

I'm sorry English is not my mother tongue, does unite mean to syndicate oneself ?

Unite means to join together. You could say you united two pieces of Lego when you snap them together, or when people join in a group it can be called uniting them. The USA is the United States of America because the different states joined together into one nation.

My apologies if there was a misunderstanding over language. Your English is good enough that I had assumed you were a native speaker

Ok that's what I wanted to say. We are all voluntarily united by the same brand of smartphone we buy, why not the same for a healthcare / others benefits groups ?

I gave an example. There could be a franchise of co-working space / hotels / resorts all over the world for nomadic or independent people and they would do the bargaining for their clients.