Try it sometime... My name is somewhat common, but not even close to "John Smith" common... but even at about 1:20,000 or so I've seen a few conflicts just from my name. Another me was born the same day in the state I reside in... I've had a few things on my credit history get tangled up over it.
I've also met two others with the same name, purely coincidentally, not related. I worked on an access/security software team at a major bank (about 350k employees internationally at the time), I found 3 bugs just by being me. Since even SSN/Tax-Id varied, there were several ways to match identity and I had conflicts in a couple of them with other employees. Last Name + last-4 of tax/ssn/national-id (for whatever country the employee was in) was one of them. I don't recall the other two right now, been about 15 years.
I've also met two others with the same name, purely coincidentally, not related. I worked on an access/security software team at a major bank (about 350k employees internationally at the time), I found 3 bugs just by being me. Since even SSN/Tax-Id varied, there were several ways to match identity and I had conflicts in a couple of them with other employees. Last Name + last-4 of tax/ssn/national-id (for whatever country the employee was in) was one of them. I don't recall the other two right now, been about 15 years.