Last post I swear.
I am saying, have said, a few things you ought to take together to understand me: Kanji is more complicated than the alphabet. But kanji's benefits aren't related to how complex it is to write. Also, I feel that the complexity of kanji doesn't have to make it hard, even if compared to a letter it's 'harder' in that it requires more effort. In fact, some theories, such as the 'levels of processing' effect, suggest that the more elaborate and meaningful the information you encode and rehearse in memory, the easier it is to learn than simpler items--while a kanji vs. a letter doesn't compare, a kanji+kana vs. a string of letters does. I think the methods we use to learn kanji and Japanese in general, images and muscle memory and audio cues, relate to that, and can be used by natives. In fact, I posted elsewhere a link to some sort of 'personal visual cognition' system that uses something similar to the Heisig method, encouraging learners to chunk the radicals into larger and larger pieces until they perceive it as a whole. Similarly I posted links to research on 'orthographic satiation' which suggests kanji are already processed as gestalt wholes, so I think it's on the right track to focus on new ways to combine primitives/radicals until they're encoded as icons.
Science is often shaped by preconceptions/hypotheses, until new research questions the dominant models and is replicated. This has been happening with paradigms for 'reading', ie how word meanings are accessed. But in the '70s, I believe someone named Coltheart did research on 'deep dyslexia' and from there formed a dual-coding model that's been improved upon and experimented with over the years. There's other models such as PDP (parallel distributed processing), integrationism, interactivation theory, whatever. Easily Googled. Researchers often used to think it was purely phonological mediation, ie you could only read and get to meanings through sound. That was based on alphabetic orthography research.
Kanji doesn't operate that way--from many studies that I've read, once you've learned a word with kanji, it--even as kana are processed like letters--is processed more as a visual icon in the brain, and is used to directly access meaning even while it also triggers the sounds you've learned that go with it in context, and even as those sounds also trigger meaning--these routes all interact, depending on how you've learned the words--on a general level. Those are my references to visual-semantic, or orthographic-phonetic, et cetera. Easily Googled.
This 'learning' dependence on how you map script/meaning/sound, by the way, relates to my recommendations to, from the onset, try to integrate senses and suchlike in an SRS. Closely related to conceptions of working memory. We learn better through the integration of multiple senses.
The 'pattern recognition' and 'priming' terms I've referenced is related to how you take in words in context. For example, reading and having the initial kanji trigger semantic associations even as you're processing the rest of the okurigana or other kanji in the compound. I've also recently read about 'cueing' as easing cross-script (kanji/kana) switching during continuous reading.
I don't know how aware natives are of all this any more than English natives can tell you about their reading process, but I know native Japanese have done most of the research I've read. Non-native research I've encountered is mostly on the alphabet, or the ones that were on kanji/kana by non-natives were way back in the '70s/'80s, and closely linked to alphabetic models. Since then, as I've read the psycho/neurolinguistic research, the 'dual coding' model (or 'triple', depending on how you interpret it) seems to have gained dominance. But that's going by my Googling and access to what's online.
So yes, kanji is hard-er if you strip it down to just its orthographic complexity, ie a bunch of strokes vs. a few lines making up a letter or kana, at which point you can say 'oh it's just an overblown alphabet letter' or dismiss it as not being worthwhile. But you should take into account how it relates to words as you learn them, within the system--educational and the media ecology people encounter, as it's used, and I think cognitive research suggests it's quite valuable. I've also read 'anecdotal evidence' that Japanese folks sight-read very easily using kanji. In contrast, we're more dependent on individual letters with strong sound mappings that mediate our access to what words mean. (Edit: Apparently this got cut before

It's physically impossible for alphabet readers to process words as icons--even the smallest most common ones--this is the current model for reading letters, so each letter must be processed independently and slotted for that heavy phonological mediation. See that Nature article I posted or Dehaene for more.
I feel that if you put together how the brain works, how the brain processes the scripts, and how adaptable learning methods are, and even if strictly speaking you can look at the education system and say 'they're not taking advantage of it' and that's true--this doesn't touch on the *potential* of a logographic/phonogographic system, of Japanese to be easier, after the initial stages of learning the kana. Whether it's easier or not hasn't been quantified, only suggested according to the logic of the alphabet being simpler, then hand-picking sociocultural issues abroad as representing definitive, universal proof of kanji's unjustifiable difficulty.
Likewise, I feel that writing has *never* been subordinate to 'speech', except insofar as people treat it as inferior. For me, that's basic logic, but in terms of the history of writing see perhaps David R. Olson's ch. 4 in The World on Paper, or look into theories about language/the mind. Also see Florian Coulmas or Roy Harris. I wrote on this in the "Why AJATT does not work for my listening skills" thread as well (p. 5). The entwining of literacy/speech since the invention of writing, how it shapes the mind and language, rethinking literacy as 'writing what you mean', even while acknowledging writing's interaction with sound.
I'm not sure how natives use Japanese to express their thoughts, but I imagine that it's physically and abstractly possible to expand the way we communicate by embracing the medium and its different uses of the senses and thus how we internally represent these transmitted thoughts, rather than imposing a perspective on it that neglects how it's actually processed as a writing system.
Edit: Oops, double-click got stuck and cut away some text earlier, hehe.
Edit 2: My next post on the topic will be about 50-100 links, then I'll drop the topic and leave people to conceptualize kanji/writing on their own...