Hello, I'm the author of this piece. It's a very good question, and the answer may simply be that script systems are inferior, but anecdotally I would say there are two advantages:

First, it makes the etymology of the script is very apparent. Often etymology in for example English is very obscure, and requires great leaps of imagination and inference to make the connections. Compare that to the character 灣 referred to in the piece, which means "bay" and contains the "water radical." The etymology can be made more clear in this way.

Second, the script is agnostic to how the characters are pronounced. This is what has allowed it to be used for several languages in China (often inaccurately referred to as "dialects")—which are often pronounced completely differently—for hundreds of years.

That said, there are clearly many, many disadvantages, and the main thing preventing change may simply be inertia.