Because what you do isn't what you say. Plus, action can happen at the same time as dialog, and frequently does. Just to make things more exciting. :)
When I'm working, or even talking about them, I tend to divide books into two categories of What Characters Do. This might be a holdover from reading lots of dramas, possibly -- but if you think about it, that's how plays are. Action or dialog. Doing or speaking.
There's actually more categories, but as I haven't got OSC's writing book handy, you're stuck with my categories today.
So my two categories for queries tend to be dialog and narrative. Narrative is a grand sweeping term. :) Essentially it's my shorthand [for "not dialog"].
But the real reason action tags don't replace speech tags is that they're not clear. Just because action is by a speaker... doesn't mean the nearby speaker said that.
I danced away from him. "That's not right!" He moved toward me again.
Who said that? Do you know?
Nope. You could say that the narrator said that. You could hope that the narrator's action makes that clear.
But it's really not.
I danced away from him.
"That's not right!"
He moved toward me again.
Okay. We still don't know who said that. In fact, now the dialog is floating even more; it could be either person, it could be someone else, it could be a ghost for all we know, or someone interrupting the two characters we can see, or...
Action is not necessarily tethered to a speaker. That's why we have speech tags, they identify characters.
The whole point of having speech tags is to make it clear for the reader. They identify those spectral voices hovering in the vasty deeps of story. Don't make readers work at guessing these things. Don't remind them this is a book.
Readers do not see speech tags per se -- remember that these take the place of the voices we aren't actually hearing -- but oh! They DO notice when no speech tags are there.