I don't know much about mixed methods/synthetic phonics etc. and am only referring to the part where OP writes 'how necessary the storybook pictures are' and only based on my very limited experience of discovering reading with pre-school DS.
What I find is that the pictures in his books (he has read all 12 stage 1+ songbird phonics books and is now on stage 2 of the same series) are incredibly important. NOT because they provide him with clues as to what the words mean which he doesn't recognise yet (he decodes those words by sounding them out). But rather, because they provide him with background and depth to the story. Let's face it, a story that goes 'I am top cat. Am I top cat? I am! I am! I am top cat. Am I top cat? I am! I am! Pop! Am I top cat?' (that's the whole text) is neither very meaningful nor enjoyable, all by itself. DS would never have become enthusiastic about reading without the images. Thanks to the images, this simple story has become very exciting, DS loves re-enacting it by climbing on the table/windowsill (sigh) or pretending to fly away with a bunch of balloons, and he loves discussing the faces on all the different cats. He reads the story 'with expression' but the expression needed cannot be inferred by the text alone, instead it relies heavily on the images.
And yet, the pictures do pose a few problems, particularly regarding re-reading the same story: a) DS memorises the stories very quickly, and the pictures provide him with the few prompts he needs (if he needs any) to avoid actually re-reading. And b) if he cannot recall the text that goes with a particular page, and starts reading, and gets to an unfamiliar word, he won't sound it out again, but will first search the picture for clues, sometimes in combination with the first letter of the word. Knowing the story already, means that he is usually successful with this strategy; but obviously it means he doesn't practice sounding out, but instead uses 'educated guessing'.
On balance, I would not want to 'lose' the images in his 'learning to read' books. I believe (please do correct me if this is wrong, it is just an assumption on my part) that enjoyment of reading is the one key ingredient that overrides everything else - with it, many if not most children will eventually learn to read no matter what method is used, without it, many children will struggle to learn to read, again no matter what method is used to teach them. Given that when you are just setting out in your learning to read journey, pictures can make all the difference between boring and hard work on the one side, and fun and enjoyable on the other side, I would opt for images and do agree that they are very important. If it means that DS applies a kind of mixed methods rather than just sounding out, when confronted with an unfamiliar word, well I can always encourage him to sound out, but I won't destroy his enjoyment by forcing him to sound out/preventing him from looking at the pictures.
Once a child has advanced past the stage where books are limited to particular sounds/letter patterns, or to simple sentence structures, or to simple contexts, or to very short book lengths, I suppose images would become less important, as more meaning can be conveyed by the words alone. So I would give less importance, in general, to the images. And yet, I would still follow my child's 'enjoyment' - if they only wanted to read comic books or other books with lots of images, I would let them, as long as they are reading and enjoying it.