[Barrin92]

>have to be learned totally separately seems to be inherently cumbersome in some ways.

It also has quite big advantages. Because writing systems tend to be highly standardized meaning of most characters has changed relatively little, so Chinese people can read ancient texts with aid of a bit of classical Chinese. And this also works across space, China has a lot of mutually unintelligible spoken dialects but pretty much everyone can understand the meaning of written Chinese. And so can even Japanese or Korean people.

In contrast spoken language tends to change so quickly that phonetic writing systems can rapidly become completely unintelligible. Old English is practically a foreign language. Probably nobody understands that "Hwæt. We Gardena in geardagum" means "Hey! We the Spear Danes, in years gone by".

[BrenBarn]

The problem with these advantages is that most actual uses of words depend on some amount of context, and only a relatively small set of word+context combinations can actually work across languages that way. It is like the equivalent of doing a word-by-word translation.

Another way to put it is that this is essentially no longer "writing language", it's some alternate form of meaning representation. Language is not just a sequence of independent words.