How much traffic are you getting with that setting?
Again looking at the monitor logs, the pattern of the score ramping up to slighly above 10, then dropping below 10 again quickly suggests that the issue is most likely related to the traffic volume (actually, probably more the packet rate) you get.
As @NTPman asked, info about your local infrastructure and uplink type would be of interest.
I note that ICMP echo requests (pings) to your IP address are being blocked, which limits a bit the ability to troubleshoot from the outside.
But you can run a ping to some typically well-connected, nearby destination yourself. My guess would be that latency, jitter, and possibly also packet drop would increase in line with the server exceeding a score of 10.
I’ve quickly compiled a list of Internet users per number of servers in a country, and unfortunately, South Korea does not have a good ratio. (Note that this is only a very rough indication, as, e.g., users may have multiple devices, clients often use multiple servers, some devices use non-pool servers, it looks at IPv4 only, …)
| Country | Internet users* | Pool servers** | Users per server |
|---|---|---|---|
| Belgium | 10021242 | 20 | 501062 |
| China | 1102140000 | 33 | 33398182 |
| Germany | 77794405 | 498 | 156214 |
| Philippines | 73003313 | 9 | 8111479 |
| Singapore | 4821119 | 25 | 192845 |
| South Korea | 49421084 | 9 | 5491232 |
* List of countries by number of Internet users - Wikipedia
** as of about 2024-10-14 ~19:15 UTC
So might be a chicken-and-egg problem like in other countries: There are too few servers in the zone, so a single server gets too much traffic. That prevents adding more servers to the zone, which would be needed to alleviate the problem. (Unless there are other reasons as well that hamper people running their own servers, like in China.)
Currently, like finally happened in China recently, big infrastructure providers would need to step in to take the brunt of the load. Seems anyhow the case in Korea, where four servers seem to take most of the load (at least when looking at the frequency with which server IP addresses are being returned by the pool):
The issue of underserved zones is actually one of the most pressing issues that in my view needs to get solved by the pool: That users are not strictly locked to only access servers in their own zone by default. There are multiple cases documented in this forum that highlight different kinds of issues this is causing.
It’s been silent on that front recently, not sure whether that is because the issue was solved (like for the China zone, where a big infrastructure provider stepped in), or people just gave up because of lack of response from the pool (like possibly for the Philippines or Vietnam zones).
Note that the widespread suggestion to simply use the global pool pool.ntp.org does NOT address the issue of clients by default being locked to servers in their own zone only. That fact is just not that obvious as with explicit use of a country zone, but well-documented. Also, that suggestion would at best help clients get better service, but not server operators of overwhelmed servers, as they have no way to control how clients are getting configured.