When an offense isn't working up to snuff, there's always a discussion about play calling. I understand that and wonder about the play calling myself but perhaps the more important factor in our sputtering is the execution of the plays called. You try to establish a running game, and it isn't working, but when do you abandon it? I've seen running games bog down and then start to work. You could be making a mistake by abandoning it too early. Maybe they were trying to tweak the running game before giving up on it. Looking back, it's easier to see clearly what should have been done and when, because we see what didn't work. What we don't see is whether the other thing would have worked better. Not saying we shouldn't have tried something different, but just saying it's an easier thing to see in retrospect than in the moment. I've thought one aspect should be minimized for another only to see the thing I thought should be abandoned start to work. And though I'm a rank amateur, I'll bet more astute fans have had the same experience.
To your point, I think that's why it's called "establishing" the run. Running the ball is more likely than passing to wear down your opponent's defense, but only after enough attempts. Thus the run game often works better in the third or fourth quarter. Unfortunately for us, we got down by two scores and had to play catch-up by passing more.
As fans, we are often quick to judge and overreact. When a play fails, it's easy to go back and say "Well I would not have called that." As you said, it may have failed due to poor execution rather than a bad choice of play. Also in today's game, most skill players have choices of what to do and when to do it depending on things such as the defensive alignment as well as individual defensive player actions. It's really hard for an uninformed observer to tell exactly what should or should not have occurred on many plays.
For example, I thought the failed fourth-down conversion by Carrie was a called run up the middle. I may have yelled at the TV. King explained that it was an RPO with a give read based on the defense. I still don't like the call, but at least it had other options.
Edit to add: "Run The Bawl" had proven to be highly successful and a key to our winning going back at least to the latter part of the 2023 season. Perhaps it's become less useful now that opposing coaches know we're going to do it, but I can certainly understand Faulkner et al wanting to lean on it at the start of the game.