I don’t have the studies at hand but I don’t think it’s such a difficult notion to accept. For starters, there are more symbols than letters, which means you have more things to learn.
But the important thing is how symbols/words are processed. For any given concept, we might have the symbolic representation, the auditory representation and/or the pictoric representation. The good thing about words is that, even if you haven’t seen the written word before, it maps to the auditory representation (more or less depending on the language). Kanji doesn’t (in fact, the same symbol might map to different “words” and sounds) and it’s not a very precise pictoric representation either.
This is not to say that Japanese is impossible to learn or much more inefficient. Just that it makes it harder to learn and read. In a similar way other languages have traits that make them easier or harder. For example, English is harder because of the inconsistent mapping between writing and pronunciation. French is harder than other languages because of the number of vowel sounds and how important it is to make them different. Spanish is harder because of gendered nouns and the fairly complicated conjugation norms for verbs. Of course native people get used to those things, still doesn’t mean they don’t make things harder or easier.
It is true that learning to read the kanji is harder than learning to read, e.g., Spanish. But I understood your original statement to not be about ease of learning but ease of reading (once learned). It is not obvious to me that Japanese is at a disadvantage here when we compare kanji vs. romaji within the same subject.
By the way, you might know this, but if a Japanese speaker doesn’t know a kanji, they are not at a complete loss. Words often consist of multiple kanji so they can infer from the meaning and possible pronunciations of the other kanji in the word. The context in which the unknown kanji appears helps too. And in literature aimed at young readers, they often also show the pronunciation written next to more unusual kanji (furigana). All of this is less relevant to APL though.
Usually hard to learn and hard to use are very correlated concepts. If something is hard to learn, it usually requires more mental energy to read. For an example closer to APL, mathematical notation is harder to read than the verbose equivalents. You not only need to keep the concepts in mind but also how the symbols are translated to the concepts. Maybe when you’re very familiarized with them they’re as easy and a little bit more terse, but it’s easy to slip back if you’re tired or just woke up less bright that day.
And that’s just in math, where there isn’t as much symbol density as in APL and where symbols don’t depend on context too much (it’s usually not a good practice and avoided if possible to have the same symbol having very different meanings depending on the context).
But the important thing is how symbols/words are processed. For any given concept, we might have the symbolic representation, the auditory representation and/or the pictoric representation. The good thing about words is that, even if you haven’t seen the written word before, it maps to the auditory representation (more or less depending on the language). Kanji doesn’t (in fact, the same symbol might map to different “words” and sounds) and it’s not a very precise pictoric representation either.
This is not to say that Japanese is impossible to learn or much more inefficient. Just that it makes it harder to learn and read. In a similar way other languages have traits that make them easier or harder. For example, English is harder because of the inconsistent mapping between writing and pronunciation. French is harder than other languages because of the number of vowel sounds and how important it is to make them different. Spanish is harder because of gendered nouns and the fairly complicated conjugation norms for verbs. Of course native people get used to those things, still doesn’t mean they don’t make things harder or easier.