So, does visualization form intuitions, or do intuitions lead to visualization, and which is better?
From my study of biologically informed AI and neurology, I actually think the answer is both. Obviously what follows is my opinion on unsettled science of the brain; I will skip the IMO and state how I see it.
Clusters of neurons "model" or simulate something; meaning given some inputs, they process those and send signals to other clusters (their output is input to another cluster). They "recognize" a pattern in their inputs, and signal that recognition elsewhere; either higher or lower. A high level cluster can recognize that some object is a dog, or car, or tree. A very low level cluster can recognize a "line" and a slightly higher one can recognize it is horizontal, or vertical, or diagonal (btw those are real proven neural mechanisms in the visual cortex).
Even higher level clusters recognize words, physics, facial expressions (some people are damaged in this area), and predict "the future" in the sense of what is about to happen in the next few seconds.
We do not think in either words or images; we "think" in neural impulses traveling to neural clusters. When words appear in your mind, that is in the wake of a thought, the thought was a signal, the neural clusters in your head that recognize such a signal as being associated with a word will fire, and you feel exactly the same sensation as what happens when that word has been spoken. That's why it sounds in your head like speech, but the thought that triggered that speech is long gone.
The same thing is true for "seeing" things in your imagination. Actual sights (say a mountain) trigger corresponding neural clusters that model that object (hey I see a mountain), and then that cluster has links it is going to send to ten thousand other clusters informing them of a mountain in the field of vision. They too will fire, and some of them are linked to feelings about mountains (idiosyncratic to the person). But that same cluster, because it links all things about "Mountain", also links to the word (in your language) "mountain", so hearing that word (or reading it then the cluster that recognizes it triggers the internal "hearing" of "mountain") will trigger your "everything about mountains" cluster, and can evoke the same feelings as if you saw a generic mountain. It is just a general model, of course, if you see Mount Fuji or Everest, there are more specific memories or facts involved. If the mountain is described, even if it is fictional, you can build up a more specific model of it: It is high, steep, and the west side has great ski slopes; the peak is often shrouded in cloud, it is craggy and the east slope is a favorite of expert rock climbers.
Now if I tell you this mountain has wheels, your brain will cast around for things that have wheels that could work with a mountain. Aha! (inspiration) It is a large prop in a school play, and it gets wheeled out on stage for certain scenes.
So both things can be true. Both intuitions and images are "models" of how things work. New intuitions can suggest images of things that "work" very similarly. The benzene molecule is a ring, August Kekulé's (a chemist) had a dream that led to proving this was the structure of benzene; about a snake swallowing it's tail.
So one model (a snake forming a circle) can trigger a realization (intuition) that something else is similar. Or the subconscious realization (intuition) that benzene can only form a ring can trigger a model with a "ring" component; he might have thought of a wedding ring, a bicycle tire, a gear with six teeth, etc. For whatever reason in his brain, this snake image arose and helped to bring his subconscious realization into conscious thought. There is nothing about the benzene molecule that is a metaphorical "eating", but whatever works for you, Kekulé!
When trying to solve a problem, coming across an image (or anything) that has a component useful for solving the problem might trigger an intuition; Aha, I know how this works! Similarly, working through a problem and realizing a new model of how it most likely works can bring forth an image of something that shares many other characteristics.
That is how the mind works, this vast free for all of billions of neurons sending signals to each other all the time; not in words or images but signals. The words/sounds and images follow in the wake of thoughts, and can trigger other thoughts, but they are NOT "thoughts".
Which is better?
Probably intuition leads to an image, but either way has its drawbacks. Images are often metaphorical, and metaphors break down quickly; they don't go far in explaining something new. But if the explanation (insight) is what leads to the image, then you aren't relying on the image to tell you how it works. You know how it works, and the image is an aid in explanation, it doesn't bear the burden of being the explanation.