It’s been stated that 工 asserts the sound こう when it’s used as a radical. I’m not sure if it’s every time. There are so many to look up that I didn’t want to bother. In any case, I’d noticed this with a few other radicals (traditional or not) as well:
曽 asserts そう or ぞう (I checked every instance on jisho.org).
昆 asserts こん (I checked every instance on jisho.org).
Do you guys know of any other cases where this sound assertion is across every usage?
As you noticed, it’s often not universal. This is because not every instance of a particular element is in a phono-semantic compound, or sometimes changes to kanji over time obscure the original sound relationship.