Why does Hong Kong use a different spoken and written language?
Hong Kong using Standard Written Chinese instead of Written Cantonese because  Standard Written Chinese (SWC) is the national standard. Most non-Cantonese speakers might not understand Written Cantonese
Some example:

English: &quot;I hate him very much&quot;
Standard Written Chinese: &quot;我很討厭他&quot;
Written Cantonese: &quot;我好憎佢&quot;

~

English: &quot;who ate my apple?&quot;
Standard Written Chinese: &quot;誰吃了我的萍果?&quot;
Written Cantonese: &quot;邊個食咗我個萍果?&quot;

I think Mandarin speaker would have hard time understanding the meaning of '邊個'
Actually, some less formal publications like comic and gossip column do allow  the use of written Cantonese
As for eliminate the use of Written Cantonese, it is a unreasonable suggestion. Spoken and written Cantonese are important parts of our heritage. They will not be abandoned as long as there are still Cantonese alive