Agree you've covered some of the pros of alphabet systems and cons of logographic systems, and those are totally valid. You're neglecting the other sides though, so let's balance that out:
Here's some pros of logographic systems:
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Higher information density - you can say more with less, and readers can parse it faster
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Compound words are intuitive - just put the symbols for the two halves of the words next to each other (or visually combine them in some cases)
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Symbols have direct meaning - there is usually no "sounding out" words to figure out what they mean, the symbol by itself fully encapsulates meaning, independent of pronunciation
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Because meaning is independent from phonetics, ambiguity is reduced with homophones, in that two words that sound the same still have two different-looking symbols
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Written communication can still be understood even across different dialects, and even across different languages altogether, if the same logographic system is used, and even if those logographic symbols have different pronunciations. This separation makes it possible to communicate across language barriers without having to learn a whole other language.
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Logographic systems don't have to adapt to changes in pronunciation over time, they're stable
Here's some cons of alphabet systems:
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Much lower information density takes longer to read, most people have to internally convert the visual data to sound to understand it, so it physically takes more brainpower/effort to understand written text
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Wild inconsistencies in phonetics within a language, requiring rote memorization of spelling "rules" and all of their various exceptions. Makes learning new words difficult as you can't be sure if you're "sounding it out" correctly unless you've heard the spoken word
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Meaning directly depends on phonetics/pronunciation, which can lead to confusion and ambiguity with alternate pronunciations, alternate spellings, and differing dialects (e.g. Canadian French vs. Metropolitan French)
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Learning a language that uses an alphabet system means learning it twice - the written language and the spoken language
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Homophones and hereronyms? Good luck
Also here's some food for thought. I 100% guarantee you use a logographic system every single day, very easily, without even realizing it. In fact, nearly the whole world uses it - Arabic numerals.