The type of identity theft where you live as another person isn’t common in the modern age where births and deaths are absolutely tracked accurately.
Modern identity theft is using someone’s personal information to get a credit card in their name or access to their bank account. You call up customer support and say “I’m John Smith and I need my account reset” and when they say “please prove your John Smith” you often times only need date of birth, address, phone number, email, mother’s maiden name, or something else literally anyone could find out about you. If there’s something they don’t know they can sometimes convince customer service by getting angry and yelling until the minimum wage worker decides to give the scammer access.
When people talk about online privacy, they often mean this. I’ll admit that as a kid I used to gain access to people’s emails just by looking at the stuff they posted on their public Facebook page. The answer to their password reset security question was almost always there. I never went further than that, but once you have access to one thing, you can usually get access to other things.