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Yes, the system is reminiscent of written Japanese in that way in that a word is sometimes spelled out phonetically, sometimes with an ideograph, and sometimes both for good measure if one or the other isn't viewed as clear enough.

I have heard it described as not quite an "alphabet" but more like a rebus[1] using an alphabet.

[1] https://en.wikipedia.org/wiki/Rebus

No wonder the scribes were so highly regarded

Very few, if any, real world writing systems are purely ideographic.