Because a new ID number can have security measures.
The ID number in my country has photograph, fingerprints, signature, several security measures (difficult to fake). Not so easy to steal (of course there are forgeries, but identity theft becomes much harder)
Hold on, do you mean an ID number or an ID card? As far as I can tell, the Cédula de Identidad you mention is a card, not just a number. Numbers are pretty much always trivial to duplicate. Checking a physical document kind of requires a face-to-face transaction.
"In 2009, researchers developed an algorithm that could guess an individual’s SSN with up to ten percent accuracy"
"SSNs have become available through data resellers, security breaches at various companies and government agencies, unsuspecting customer service representatives, and even public records, if you know where to look. SSNs can be bought in bulk for $1 each on private online forums, and a specific person’s SSN can reportedly be had for as little as $3.80."
I've also read about duplicates ("More than 20 million Americans have more than one SSN associated with their name."), the numbers running out (in the 2050s apparently), etc.
Some other advantages (from an IT point of view): you can validate an ID number against a central database, and get a person's given names in a unique format. Our ID numbers have a check digit, so you can validate if the ID number has been correctly entered :)
Certainly SSN could be improved by making them harder to guess and adding check digits. Other than that, I don't see how any other number scheme is any better. Ultimately there is some number that is associated with you, and is therefore useful for identity theft. Since it has to be used by people and not just computers it'll have to be relatively short and thus easy to steal.
Multiple identifiers per person is a feature, not a bug. People get new SSNs when they want to change their identity (eg, witness protection programs), or because someone stole their old one. That need doesn't go away just because you have a new numbering system.
