The reason for the presence or absence of the brief doxology at the end of the Lord's Prayer is actually liturgical use.
In Eastern-rite usage, the doxology is recited in the liturgy after the Lord's Prayer; this is probably how the phrase crept into Eastern Greek mediaeval manuscripts of the New Testament. These manuscripts are ultimately the ones on which the KJV was based. The KJV served as the Bible for English liturgy for a long time, thus becoming traditional for Protestants.
On the other hand, the doxology never made its way into the text of the Latin Bible, which was the basis of Western-rite (Roman Catholic) liturgy. So it is not understood as part of the Lord's Prayer proper in the Catholic Church.
Newer Protestant translations make use of a scholarly critical text of the New Testament. Biblical scholars stand in general consensus that the original Gospel of Matthew did not have the doxology. They believe this because the earlier Greek manuscripts don't have the phrase, and neither do early translations of the text, while there is a clear motivation for adding it in later Greek manuscripts. So the phrase is absent from the text of most modern translations (though it might be noted in a footnote).