It is a certain gatekeeping that demands some quantity of flexibility in culinary arts.

To me flexibility in culinary arts would mean that you know dishes from multiple cuisines, not just two dishes from French cuisine.

I'm willing to believe those two dishes represent a wide set of skills and knowledge that would generalize to being a generally skillful cook.

Why both of them? They are both braised meat dishes. They test roughly the same skills and knowledge. Surely if you wanted to pick two french dishes you'd pick two that cover a wider set of skills.

They are also both dishes that are highly forgiving. You can elevate them by replacing the vegetables used in the braise with precisely cooked ones in the final product, by balancing the braising liquid properly, and by getting the final braising liquid to the right consistency but this is largely procedural and involves balancing fewer different elements than sauces that involve spiciness in addition to sweet, sour, and savory.

As someone else noted, I don’t believe these skills would translate to sushi making and we’re talking about chefs here not cooks.

I think someone who knows those dishes like the back of their hand would make significantly better sushi than me. On the other hand, I'm willing to bet that someone who just makes burgers probably can make sushi about as well as I could.

Would you expect the best Sushi chefs in the world to be competitive in a professional environment to make French cuisine? My bet is no, they focused their entire career on sushi. Similarly, a professional chef who knows how to make these two dishes really well would not be able to compete with professional sushi chefs without actual training in that specific discipline.

What flexibility? The two dishes you selected are essentially variations of the same theme: a meat braised in wine with typical European produce and seasoning.

If you want flexibility, ask someone to master ramen and filo dough.