The phrase "one's logical end" refers to the eventual outcome or consequence that is expected based on reason and rational thinking. It means reaching a conclusion or result that is logical and makes sense given the circumstances. Full definition
Fittingly, Joseph further suggests that with the White Paintings, Rauschenberg enacted the evolution toward essential flatness foretold by Greenberg as the extreme, logical end point of modernist painting.4 With this flatness would come an absolute eradication of image, mark, and color. (sfmoma.org)
They were all can't miss amateurs with one logical end game: basketball stardom. (businessinsider.com)
Confrontations with others are typically brief, sometimes without logical end, and the director intentionally tones down most of the violence so that his characters can wallow in passive - aggressive detachment. (filmfreakcentral.net)