Well yes. But it is the same as like quitting smoking and drinking as a heavy abuser from one to the other day. Your next few weeks will be not so cool. On this case it will be not so cool decades
Looking here the fertility rate is declining since the 1960s, so I wouldn't say 60 years is like quitting from one day to another, they had more than enough time to tackle the problem.
I've noticed a major uptick in people referring to South Korea as just Korea.
I think the powers that be are just trying to wipe the idea of a North Korea out of people's minds. It's just Korea, and South Korea is the owner of it all. (in their minds and how they want us to believe)
Eh, it's more likely that the statistics that come out of North Korea are so few and so unreliable that there's no reason to specify that they're talking about South Korea, it's just assumed by most that they aren't talking about the Hermit Kingdom.
And fwiw the South Koreans refer to their own country as 대한민국 daehanmiguk - the Great Korean People's Country and the North call themselves 조선 Joseon (or more specifically the Democratic People's Republic of Joseon), the name of the last Korean dynasty. Neither refer to each other as "North" or "South" and they discourage the use of divided names because it implies the goal of both isn't unification.