Since it is my answer you are referring to, I will take a stab at this.
First, I would generally avoid saying that something is "bad" in writing. It is more useful to think in terms of everything having an effect. A given technique has a given effect. If it is the effect you want, it is a good technique and if it is not the effect you want it is a bad technique in your case.
Mixing dialogue and action is a technique that has certain effects. I think in many cases they are not the effect the writer was striving for. This is based on many years of reading unpublished manuscripts in critique groups and trying to figure out what was not working for me about them, and then trying to contrast these not-working passages from working passages in published books.
In real life, of course, speech and action go together all the time. In fact, it is often hard to follow the speech without seeing the action. So why wouldn't it be natural to mix them in prose the way they are mixed in life? To me, it comes down to the way that a scene is painted in prose: one word at a time.
Consider how a scene is painted in a movie. A movie director has to fill a fixed frame with a picture 100% of the time. They also have to fill every scene with sound 100% of the time. (Silence is significant in a movie. It means something. Silence is a sound, a deliberate sound.) The problem for a director is that the viewer is free to look at any part of the screen at any time. In order to make sure that the viewer pays attention to the right part of the screen the director needs to induce the viewer to look at a certain part of the screen. They can do this with various cinematic techniques, such as contrast, close ups, movement (the human eye is drawn to movement, which is why we use flashing lights on emergency vehicles), sound cues (a baby's cry makes you look at the baby in the shot), short depth of field, and pull focus.
For a film director, therefore, mixing dialogue and action makes perfect sense. The viewer can see the action and hear the speech at the same time, just like they do in real life, and the combination of the two helps keep the viewer's eye focussed on the right part of the screen.
The novelist has the exact opposite problem. They can't show the reader a picture or play them a sound. They can only present them a sequence of words. The reader's attention is always on the current word. If you want the reader to see or hear a scene, you have to enable them to build that picture for themselves in their own minds. Part of the necessary economy of prose is the most of the images the reader sees and the sounds they hear will come from their own imaginations, their existing stock of images and experiences. You are using your words not to paint the whole scene, but to provoke the reader's imagination into building the picture for themselves, something you can often do with just a few well placed words.
But there is an important limitation in prose. It is not possible for two things to happen at once. Unlike a movie director, you cannot show someone speaking and scratching their nose simultaneously. You can write:
"I don't like strawberry jam," said Reginald, scratching his nose.
But these two things do not happen simultaneously in the reader's mind because they have heard the the words before they see the scratch, and therefore the scratch comes after the words in their experience.
So while a director can do:
Speech + action
Speech + action
Speech + action
A novelist can only do:
And that has a much more disjointed, staccato feel to it. The reader is not taking in speech and action as a unit. Rather their attention is been forced back and forth rapidly between speech and action, rather like the experience of being in a busy crowded railway station.
And, this, I conclude, is why most novelists avoid mixing dialogue and action in most cases, and present dialogue as a simple exchange of speeches with only the minimal use of speech tags and maybe the odd shrug or nod (actions which, in any case, happen in serial, not parallel with speech).
Of course, if you are trying to write a scene in a busy crowded railway station and you want the reader to experience the same assault on the senses the the character is experiencing, this may be the right technique to achieve it. But most of the time this is not the effect you want.
What I have concluded, from many years of critique groups sessions, is that a lot of writers are, consciously or not, trying to write a scene as they imagine it being acted in a movie. But this usually does not work. (And it is worth noting that when books are made into movies, much of the dialogue is usually changed, because movie dialogue just works differently, principally because you have an actor to act the conversation, and thus supply much of the meaning with action and expressions.)
The nature of prose, the fact that it is impossible to do anything in parallel and that you have to rely on the reader to paint any scene for themselves, means that it is often necessary to separate things that happen simultaneously in real life and to focus on one thing for a while before switching to the next. Thus you can use description to set up a sequence of dialogue, pre-populating the reader's imagination with the appropriate setting before the dialogue begins, and then relying on that image to inform how they see the dialogue unfolding.