That likely depends on how effective we are at eliminating it in the coming months. I doubt it will become endemic in Korea or Singapore.
I wonder if even influenza could be erraticated in the coming years with mass testing and contact tracing. The lockdowns ended flu season early this year.
We'd have to eliminate it worldwide, or it would travel from country to country like the flu does.
In particular, from Mexico. There's too much travel between the US and Mexico to prevent it from crossing the border, and there are 50,000 confirmed cases in Mexico already, with roughly 2000 more being found every day.
Given the relative number of cases, Mexico should be stopping travel from the US, not the other way around.
Reducing travel from Mexico has been a popular position in the Us for decades.
Let's not discount pharmacological options. HIV doesn't have a vaccine, yet it can be fought with a proper (admittedly very complex) drug regime.
The same can be probably done for SARS-CoV-2, although we'll have to wait for specific drugs to reach better efficiency.
And I add, we don't need to make this virus disappear (it would be better, but even with a very efficient vaccine it is unlikely). If we can prevent hospitalizations (and possibly deaths), we can likely live with it like we did with many other pathogens.
If COVID-19 is in the latter category, it will be difficult to control and we'll probably have to learn to live with it, as we have learned to live with the flu causing hundreds of thousands of deaths each year worldwide.
1: https://www.sciencemag.org/news/2019/04/how-long-do-vaccines...