> South Korea is capable enough to build nuclear submarines even if the US had denied them the said facilities

Technically, yes. Politically, no.

“To produce fuel for the submarines’ naval propulsion, the ability to enrich uranium was required. However, this plan probably served two goals, since a country with enrichment capability can also enrich uranium to weapons-grade levels without significant difficulty. The fact that [former President Roh Moo-hyun] launched this plan less than five months after North Korea’s [2003] withdrawal from the Non-Proliferation Treaty (NPT) supports the possibility that his ulterior motive was to acquire uranium enrichment capability in part to enable the future development of nuclear weapons. Ultimately, Roh had to abandon this plan in 2004 amid rising suspicion of South Korea’s nuclear ambitions after the International Atomic Energy Agency (IAEA) discovered that South Korean scientists had previously conducted an unauthorized enrichment experiment” [1].

[1] https://www.csis.org/analysis/will-south-koreas-nuclear-ambi...