Debate on mixed script and hangeul exclusivity

The debate on Korean mixed script "hanja honyong" (Korean: 한자혼용; Hanja: 漢字混用) and Hangŭl exclusivity "hangŭl jŏnyong" (Korean: 한글전용; Hanja: 한글專用/韓글專用) is an ongoing debate concerning the use of Chinese characters, known as "Hanja" (漢字), in Korean orthography. It is a hotly contested topic to this day in Korea and garners the attention of many as it is an issue which concerns education from its earliest years to university. The debate itself is a question as to whether Korean should be written with Hanja mixed into the text, or purely in Hangŭl (e.g. 大韓民國를~ vs. 대한민국를~). The debate also oftentimes centres around the education of Hanja in schools, the effects of which are also debated. It is a controversial debate which concerns the orthography, vocabulary, and other aspects of the written language.
History of Mixed Script.
The foremost problem at the centre of this debate is the use of Hanja. Mixed script was a commonly used means of writing, although Hangŭl exclusive writing has been used concurrently, in Korea after the decline of literary Chinese, known as "hanmun" (Korean: 한문; Hanja: 漢文). Mixed script could be commonly found in non-fiction writing, news papers, etc. until the enacting of Park Chung-hee's 5 Year Plan for Hangŭl Exclusivity "hangŭl jŏnyong ogaenyŏn gyehuik an" (Korean: 한글전용 5개년 계획안; Hanja: 한글專用 5個年 計劃案) in 1968 banned the use and teaching of Hanja in public schools, as well as forbade its use in the military, with the goal of completely eliminating Hanja in writing by 1972 through legislative and executive means. However, due to public backlash, in 1972 Park's government allowed for the teaching of Hanja in special classes but maintained a ban on Hanja use in textbooks and other learning materials outside of the classes. This reverse step however, was optional so the availability of Hanja education was dependent on the school one went to. Park's Hanja ban was not formally lifted until 1992 under the government of Kim Young-Sam. In 1999 the government of Kim Dae-Jung actively promoted Hanja by placing it on signs on the road, at bus stops, and in subways. In 1999 Han Mun was reintroduced as a school elective and in 2001 the Hanja Proficiency Test "hanja nŭngryŏk gŏmjŏng sihŏm" (Korean: 한자능력검정시험; Hanja: 漢字能力檢定試驗) was introduced. In 2005 an older law, the Law Concerning Hangul Exclusivity "hangŭl jŏnyonge gwahak babryul" (Korean: 한글전용에 관한 법률; Hanja: 한글專用에 關한 法律) was repealed as well. In 2013 all elementary schools in Seoul started teaching Hanja. However, the result is that Koreans who were educated in this period having never been formally educated in Hanja are unable to use them and thus the use of Hanja has plummeted in orthography until the modern day. Where Hanja is now very rarely used and is almost only used for abbreviations in newspaper headlines (e.g. 中 for China, 韓 for Korea, 美 for the United States, 日 for Japan, etc.), for clarification in text where a word might be confused for another due to homophones (e.g. 이사장(李 社長) vs. 이사장(理事長)), or for stylistic use such as the 辛 (Korean: 신라면; Hanja: 辛拉麵) used on Shin Ramyŏn packaging.
Information Theory.
Proponents of the use of mixed script of cite information theory as an argument against Hangŭl exclusivity. The premise being that Hangŭl has a much lower amount of information in comparison to Hanja. Hangŭl has 24 letters: 14 consonants; ㄱ ㄲ ㄴ ㄷ ㄸ ㄹ ㅁ ㅂ ㅃ ㅅ ㅆ ㅇ ㅈ ㅉ ㅊ ㅋ ㅌ ㅍ ㅎ, and 10 vowels;ㅏ ㅐ ㅑ ㅒ ㅓ ㅔ ㅕ ㅖ ㅗ ㅘ ㅙ ㅚ ㅛ ㅜ ㅝ ㅞ ㅟ ㅠ ㅡ ㅢ ㅣ. Whereas Hanja are ideograms consisting of over 80,000 individual characters, around 2,000 of which are considered "common use" in Korea. Thus if you assume Hangŭl occurs with equal probability and is independent (which is not true as the actual probability for Hangul ranges from 0.122 for ㅇ and 0.002 for ㅋ), each Hangŭl letter occurs 1/24 of the time whilst each Hanja occurs 1/2,000 of the time. Thus, the entropy of Hangul is only 4.75 bits-per-symbol, while the entropy of Hanja is 10.96 bits-per-symbol (and 15.29 bits-per-symbol, when 40,000 symbols are considered). This means that each character of Hanja conveys much more information than each letter of Hangŭl. This data is of course not entirely correct, and in actuality certain symbols do occur with more frequency than others, and therefore the entropy will be much lower. However, this does not detract away from the finding that each character of Hanja conveys more information than each letter of Hangul as there is still a lot more Hanja characters than Hangul letters. The fact that Hanja conveys more information than Hangul has ramifications in the semantic meaning of each character. Using the word "일" as an example, composed of the Hangŭl letters ㅇ, ㅣ, and ㄹ. In only three letters there is much ambiguity this could mean 一(일) "one", 業(일) "work", 日(일) "day", or even be a grammatical particle. As shown, writing the Hanja makes it clear and obvious which "일" you mean. To take the example further you can compare Hanja to their Hangŭl pronunciation and corresponding native word, or eumhun (Korean: 음훈; Hanja: 音訓). See below:
Many times Hangŭl may appear more compact simply due to its nature of being stacked into syllable blocks. Based on the actual brevity and amount of information conveyed from an information theory perspective, Hanja is a superior means over Hangŭl. And a mixed script orthography with an optimal distribution of probability between Hanja and Hangŭl would increase the information content of writing, shortening the amount of symbols needed to convey the same meaning while maintaining ease of learning.