Opinion-time, everyone. The bug bit me while I was studying Proverbs chapter eighteen—rather odd, as it contains no “words of Christ.” But that’s where it gets interesting; Jesus Christ is God’s eternal Word in the flesh, and he authored the verbal (both the ancient, oral tradition, and the written) Word of God from start to finish (John 1:1-18, 2 Timothy 3:16). In view of these facts, can any part of God’s verbal Word not be Jesus’ words? Highlighting Jesus’ words in the gospels implies that they are somehow more reliable or have more authority than the balance of Scripture, which is theologically unsound.
That said, I understand how novices in Bible-study might prefer “Red-Word” Bible editions, but I would also caution them against assigning those red words undue significance. There is a heresy that says Jesus’ words carry divine authority, but the rest were written by (sexist) men, most especially that male-chauvinist-pig, Paul.
To deny any part of God’s Word is to deny its Author, and we wouldn’t want to do that, would we?