The most important muscles used to generate space when on mount bottom are the glutes, hamstrings and lower back (i.e. the muscles invloved in bridging and shrimping) and sitting low means you are sitting right on top of where all these muscles connect. The action of bridging and shrimping is in essence movement of the hips. By assuming a low mount you are connecting to that movement.
Of course, there are ways to counter that but you'd be ill advised to go for armbars straight from low mount as your own hips are far from the arm pits and the elbow. If you're gonna lock down the low mount you are preparing for something else such as americana or sleeve chokes...etc.
To successfully attack with straight armbars (irrespective from which position - mount, side, back, knee ride...etc.) then your chances are higher if your hips are closer to their upper arm, eg. in high mount. Sitting on the chest is very stable (if you know what you're doing) and opens for smoother transitions (e.g. to the back or knee ride)
As for the wrist grab I assume the demonstrator is thinking from a trained-vs-untrained perspective. If you mount on someone who doesn't know what you are doing to them, they won't expect the armbar. I'm not saying I never grab the wrist and always go for the elbow hook. I'm just relaying what the setup tells me.
Breaking gable grips and other armbar counters is not rocket science. The biceps crush is a good clever alternative but it's exactly that: an alternative to the armbar. You should aim to finish what you started intelligently.