I understand that. I don't understand why not. The rule doesn't make sense to me.
Well, because it's just not correct. You can just not have speech tags, but you can't use action verbs as speech tags.
"I need a new grater," Mark said as he pulled up a chair - this is the more correct and easier to understand version, at least to me.
"I need a new grater." Mark pulled up a chair - this is fine, although a little awkward - sounding.
"I need a new grater," Mark pulled up a chair - that's not okay, because it makes no sense.
You need the speech tag included for it to make sense; authors can't just assume that readers will make the mental leap themselves. Even though I can do that if needed, it's mentally exhausting and makes me really not like the book.