There are many who advocate a verse-by-verse approach to preaching. Some entire denominations take this approach. Some (wrongly) define expository preaching by this form. Here are Steve Mathewson’s lists of strengths and weaknesses of the approach.
Strengths. 1. Verse-by-verse sermons dig deeply into the text, thereby countering the contemporary trend toward biblical illiteracy. 2. Verse-by-verse sermons lead the preacher to follow the contours of the text rather than an artificial outline. 3. Verse-by-verse preaching has a tendency to real the author’s intent rather than imposing an idea onto the text.
Weaknesses. 1. The verse-by-verse approach does not serve all literary genres of Scripture equally well. 2. The verse-by-verse approach sometimes results in sermons that lack unity, wherein there is much analysis, but little synthesis. It is possible to obscure the flow of thought in a text by giving emphasis to every passing detail. 3. There is a tendency in verse-by-verse preaching to overload the sermon with raw data and short-change application. 4. Verse-by-verse preaching can slow the preacher’s pace so much that a congregation does not get to hear the whole counsel of God over a reasonable period of time.
(See Mathewson’s chapter 110 in The Art and Craft of Biblical Preaching, pp407ff).