I don’t know who decided that “said” is an invisible word but they are wrong! It’s also a telling word.People don’t notice “said.”
Other words are “telling” words.
I had the pleasure, and I say this tongue in cheek, of revising a manuscript in which the author only used “said.” The piece read like a Dick and Jane story without pictures. I’ll admit there are other issues with this author’s writing skills but every dialogue was “he said,” “she said,” covering pages of writing. It was boring and unimaginative. Readers need to see the picture and that takes more than using “said” as a dialogue tag. Why do we take away from the English language in the first place? It's so limited in comparison to other languages to begin with.
I see parallels with my Christian walk and my writing ministry. I can say I’m a Christian and quote scripture but at some point there has to be a picture—my life has to show the meaning of the words. I have to live my faith.
So whether it’s in a manuscript or in living, “said” may not always do the job and is definitely not invisible.