Start Hanja Script language for Korean
You're alone... By IETF's definition in the IANA database for BCP47, [ko]=[ko-Kore]:
%% Type: language Subtag: ko Description: Korean Added: 2005-10-16 Suppress-Script: Kore
[ko-Hang] is therefore a subset of [ko]=[ko-Kore]
And under the ISO 15924 standard, [ko-Kore] is perfectly defined as Korean in the [Kore] script mix, perfectly defined by ISO 15924 as all scripts used for Korean, past or present, which include Hangul+Hanjas.
The problem you have is the mapping [ko]=[ko-Kore], while you want [ko-Hang]. But this is not what is in the IANA database and the BCP 47 standard (which is also THE standard for all web applications, including HTML, XML, CSS, SVG, and almost all programming languages, as well as almost all I18n libraries used in applications that are not restricted to just some ISO 639 part).
The situation is exactly the same for Korean as it is for Japanese [ja]=[ja-Jpan]: here also modern Japanese can no longer be written only with Kanjis. But this "only" is not relevant for saying that modern Japanese is [ja-HrKt] (though it is possible to make some approximation to it to drop Kanjis for some limited usages). As well modern Korean is a mix which may be written using Hangul "only", but there's no such restriction enforced, except for some limites usage, like in the South Korean government official documents). Koreans can legally use Hanjas as they want, and they do (including the South Korean governement, otherwise it would not even be an active member of the joint IRG working group for encoding sinographic scripts in Unicode/ISO/IEC 10646).
And Korean [ko] is not limited to just its current modern form, it's an umbrella for all variants including historic forms, and variants used in North Korea, and cultural variants that are still living today: Hanjas are not dead.