Limitation of English
This issue about the article may be more about the limitation of English language rather than accuracy since English forces a dichotomy between definite and indefinite. The use of the definite article "the" indicates that the noun is specific. For example, the sentence "The cat is on the mat" refers to a particular cat and a particular mat. The use of the indefinite article "a/an" indicates that the noun is non-specific. For example, the sentence "I saw a cat on the mat" refers to any cat and any mat.
This translation dichotomy between specific and non-specific nouns is not present in all languages; it is unique to certain modern European languages.
To have a more accurate and fair translation, I'd prefer the indefinite "a Christ", or "an anointed one" here (Greek OT, LXX has 41 occurrences of Christ/Χριστός). The traditional English Bibles have rendered it definite. Note, in the old traditional translations "Christ" is still definite since it is used as a title and the phrase ends with that noun: "to go and repayre Ierusalem againe, vnto Christ (or the annointed) prince: there shalbe seuen weakes". Thus, the English translations are forced to either use definite or indefinite article, the same problem has been noted about translating "the law" (Greek Nomos).
Revised Standard Version (RSV) in 1952 departed from the traditional translation to make the "Christ" indefinite, to give a more accurate translation, which has been followed by a modern versions like the ESV, NABRE, NET. To present a specific interpretation as translation would predispose the generations with a narrow text and interpretation. It would create shallow and naive view that there can be no Saviour and Messiah besides Jesus, as a result these naive believers would burst into a fit of rage when one calls the Kings like Alexander the Great, Cyrus or Donald Trump as our Saviour/Christ/Messiah, thereby accusing others of "blasphemy". The ambiguity in the more accurate "a Christ/ an anointed" would also facilitate potential dual fulfilment of the prophecy.
The point about accuracy is nicely described by Claudemiro Francisco Mariottini in Rereading the Biblical Text Searching for Meaning and Understanding · 2013, p. 146
In Daniel 9:25 the word “the” as in “the Messiah is not present in the
Hebrew text. Thus, the Hebrew text s talking about “an anointed one” one
who could be a priest or a king. However, because the translators of the
KJV used the word “Messiah?” with a definite article and a capital letter M,
Christians immediately say: “there is only one person who is ‘The Messiah;
and that person is Jesus Christ” Thus, readers of the KJV are predisposed
by the translation to see Jesus Christ in Daniel 9:25. However, if one adopts
the translation of the RSV, the whole idea of the text changes.
‘The RSV reads: “Know therefore and understand that from the going forth of the word to restore and build Jerusalem to the coming of an anointed one, prince, there shall be seven weeks. Then for sixty-two weeks it shall be built again with squares and moat, but in a troubled time.”
E. J. Young, in his commentary on Daniel, follows the translation of the RSV. He translates the words in question: “unto an anointed one, a prince” Now, this is a good translation. But then he inserts this comment: “The fact is that there is only One in history who fully satisfied the two essential requisites of the theocratic king, Jesus who is the Messiah” Now, this is a bad (though some would say good) interpretation and this is the same principle that influenced translations of Daniel 9:25.
In discussing Daniel 9:25, I have not made any reference to date o authorship. This is irrelevant when it comes to the issue of translation. A commentator may inject his theological bias on the interpretation of the text and decide who that anointed one was. However, the translator does not have that luxury. The translator mast follow the intent of the original author and avoid making the decision of who in history fully satsfis the two essentials of leadership mentioned in Daniel 9:25, as the translators of the King James did.