Does the text not imply that Seth was in the image of God, via Adam (Gen 5:3)? But this is true of everyone; so why mention it? Is it important?

It is probably more important than it might appear at first. There are two points to be made here, one positive and one negative. The positive point is that, if Adam was created in the likeness of God, and Seth was begotten in the likeness of Adam, then “the likeness of God” seems to have been passed down along the line of the people who “began to call on the name of the Lord.” (Gen 4:26) This same line, as described in the rest of Gen 5, gave rise to two men who “walked with God”: Enoch and Noah. It was through Noah and his family that mankind was preserved from total destruction. Notice, about none in Cain’s line is it said anywhere that they were begotten in “the likeness of” God. Cain and his family had abandoned God; so he abandoned them. This brings us to the negative point: while “the likeness of God” is something pure and holy, that likeness was to an important extent lost, though not entirely, so that “the likeness of Adam” was something “earthy” and sinful: “as by one man sin entered into the world, and death by sin” (Rom. 5:12) as Paul puts it. Thus there is a subtle but clear contrast between the line of Cain and that of Seth, reflected later in such Pauline statements as this: “As is the earthy, such are they also that are earthy: and as is the heavenly, such are they also that are heavenly. And as we have borne the image of the earthy, we shall also bear the image of the heavenly.” (1 Cor. 15:48-49)