There will never be a problem with that in Sweden. They're averaging 328 births per day. They'd need to increase their population from 10 million to the size of the United States to bump up against that limit.
Sweden has added two million people in the last half century. In net terms, essentially all of those two million have been immigrants rather than born in Sweden. They're de-populating when you exclude immigration, because their birth rate is so low.
10,000 people per day would be like Sweden adding 1/3 to its population in the next year. That's never going to happen. They're #166 when it comes to birth rate. Based on their population gain rate, they'll need to worry about the four digit limit in about 2,000 to 3,000 years give or take.
Actually, it already is a problem. According to this article, around 2,500 people have been assigned a personal number which differs from their birthdate. [1]
The last digit is just a checksum digit, so we're left with 3 digits per day. But that still would give some leeway for each day. The problem seems to be that some immigrants have been assigned a default birth date (Jan 1 and Jul 1) as their exact birth date is unknown.
Another issue which is not mentioned in the article is that we're only using two digits to encode the year (i.e. YYMMDD-XXXX), which causes problems now that many live to be 100+ years. Most banks and other places now requires you to enter a four digit year, even though that technically is incorrect. The correct way to annotate that someone is over a hundred years old is that the dash changes to a plus sign (i.e. YYMMDD+XXXX), although I've never seen that implemented anywhere.
Sweden has added two million people in the last half century. In net terms, essentially all of those two million have been immigrants rather than born in Sweden. They're de-populating when you exclude immigration, because their birth rate is so low.
10,000 people per day would be like Sweden adding 1/3 to its population in the next year. That's never going to happen. They're #166 when it comes to birth rate. Based on their population gain rate, they'll need to worry about the four digit limit in about 2,000 to 3,000 years give or take.