Important : This bank is an Internet-only bank in Korea and since banks don't allow foreigners to apply for an account online, You must be a Korean citizen to become their customer.
K Bank (케이뱅크은행) is the first online bank in Korea.
This bank is founded by Wooribank(우리은행), KT, NH Investment & Securities(NH투자증권), GS Retail(GS리테일), Hanwha Life Insurance(한화생명) and more. Account plans and check cards from this bank usually come with their products.
The reason why they don't accept foreign resident customers : In summary, it's because of the govt policies. The Financial Services Commission in Korea conducted and regulated the online application system and its policies and guidelines, and all banks in Korea must follow them. The policies and guidelines may have some directions including what kind of information banks need to collect from their new customers and what kind ID cards are valid for the system. Currently, the policies and guidelines are regulated to be working with the only Korean citizens' identities. There are no guidelines for foreign residents, hence, the banks can't accept foreign residents customers online, even if they actually want to do. If you really want to change this problem, it'd be better to appeal to the FSC or other supervisory agencies, so that they can realise your inconvenience.
Update : The FSC announced changes on the guideline to allow foreign residents to open a bank account remotely. The bank will possibly accept foreign customers in 2020.