Instead, the Prophet held the view that the new scriptures corrected some of the mistakes in the original Biblical texts. Furthermore, he specifically stated that he did not correct everything that he could have corrected in the translation process. However, the scripture as written was correct enough to get his point across. Likewise, any errors in the text of the Book of Mormon were deemed unimportant as the text was sufficiently plain for its stated purpose. Likewise, while the Prophet never finished the JST, he deemed the work sufficient to merit publication.
Several reasons come to mind.
First, throughout his life, Joseph Smith faced constant persecution. Therefore, the circumstances of his life did not permit him to do so. Keep in mind that despite the adversity in his life, he did manage to give us more scripture than any other prophet or apostle, including Moses and Paul. As we obey the truths we have, we are given additional knowledge. Through Joseph Smith, the Lord has given us a tremendous amount of new knowledge.