Why Japan still refuses to test everyone (or at least all Japanese passengers) on that Diamond Princess cruise ship is just strange at best.
That cruise ship has put lot of strain on Japanese resources from testing to treatment. Once a persons has been tested positive, preparing hospital to accept that patient is another can of worm.
According to their official announcement last week [1], South Korean government is currently able to test 3,000 persons per day and will be able to test up to 10,000 per day by the end of February. Even after accounting for false positives this would be enough to test everyone on a cruise ship.
[1] http://ncov.mohw.go.kr/tcmBoardView.do?contSeq=352788 "그동안 진단검사 기관을 시도 보건환경연구원에서 민간의료기관으로 확대하였고(2.7), 검사가능 물량도 대폭 늘리고 있으나(1일 200명→3,000명), 2월 말까지는 생산업체, 민간검사기관 등을 확대하여 현재의 3배 수준인 하루 1만 건의 진단검사가 가능하도록 확충할 예정이다."
Edit: see additional information in reply comment by @lifthrasiir
> 그동안 진단검사 기관을 시도 보건환경연구원에서 민간의료기관으로 확대하였고(2.7), 검사가능 물량도 대폭 늘리고 있으나(1일 200명→3,000명), 2월 말까지는 생산업체, 민간검사기관 등을 확대하여 현재의 3배 수준인 하루 1만 건의 진단검사가 가능하도록 확충할 예정이다.
> Meanwhile it was made possible to perform tests not only from local Health and Environment Research Institutes but also from private medical institutes as of February 7, and the diagnostic capacity has greatly increased from 200 to 3,000 per day, but we plan to increase it further to 10,000 tests per day by the end of February, through more diagnostic kit producers and more participating private medical institutes.
The capacity might seem unrealistic, but the linked website has a live counter for the number of diagnoses in progress ("검사진행") and that reads 558 as of today. And that is not a stale counter; some daily report [1] has a table that reads 2,736 candidates were tested (negative) from 2020-01-03 to 2020-02-11 09:00 AM, and 4,054 were tested to 2020-02-12 09:00 AM, yielding at least 1,300 actual tests completed that day, and the counter remains relatively stable (992 back then). Probably it is true that 3,000/day figure is theoretical, but 1,000/day is very real.
> In the meantime, we expanded the diagnostic testing agency from the Institutional Health and Environment Institute to the private medical institute (2.7), while the number of testable items has been increased (200 → 3,000 per day), but by the end of February, The company plans to increase the number of diagnostic tests to 10,000 times a day, three times the current level.
IIUC it says 3000 per day. (I'm not sure if it's the peak capacity or if they can sustain it for long periods.) Also, it looks like they are still working to raise it to 3000 and expect to reach it soon, not the current capacity.