So what prevents people applying for loans or doing identity theft, in other countries?
Key difference might be that most countries have centralized Federal ID document. The Americans never allowed the government such a power, which is a tremendous idea. But they did concede to an ID number through a federal tax entity which de facto served as an id number. Turns out one disadvantage there is that a document is easier to prove ownership of than a number.
To sign on for a house, marry, claim a child as yours etc you need witnesses where I live. Web of trust I guess?
If someone takes a loan in my name and I don't receive the money it is not an identity theft it is fraud and the victim is the bank not me.