Sorry for the huge quote, but I felt that it was written really well:
There are two reasons given why a kittel is worn:
1) The kittel, being a plain white garment, symbolizes purity from sin.
2) A person is buried wearing a kittel. Therefore, when a person wears a kittel he feels humble and remorseful for his sins, remembering the day of death.
According to reason #1, the kittel would only seem appropriate for Yom Kippur, when we are cleansed of our sins, but not for Rosh Hashana. Reason #2 is also not totally applicable to Rosh Hashana; although Rosh Hashana is a day of repentance, it is also a joyous holiday of solemn celebration and one should not display undue sadness.
In some communities the kittel is in fact worn on Rosh Hashana by all congregants. This custom is mentioned by Mateh Moshe and has its source in a midrash which describes how the Jewish people wear white on Rosh Hashana, confident that their sins will be forgiven. Perhaps the custom you mention, namely that the shaliach tzibbur, ba'al tokeah and ba'al korei wear a kittel is based on this midrash, due to their crucial role in the Rosh Hashana services.