I have probably mentioned it here before but I don't think there is enough creativity and even "cooking" involved in sushi to warrant comparison to haute cuisine or Japanese haute cuisine for that matter. I think they could award 1 star to the best restaurants; the ones that receive 3 stars today.
You see this for wagyu. The top steak houses get one star. In both cases we could say that they offer the best ingredients and therefore get the single star.
Since sushi means sour rice then, yes, the rice preparation is important and distinguishes top sushi as well but I don't put this in the category of haute cuisine.
Re Abasque. I looked at that place since it is in my neighborhood and it got its star in recent years. (I typically look for new Michelin restaurants.) I was indeed mystified why that type of food gets a star.
I recently went to a new French one star, Liberte a Table de Takeda. I thought it was good and maybe deserved a star. But if you compare to, for example, Hostellerie de Levernois in Beaune (one star) then no way. I think this latter restaurant might even deserve two by French standards.
p.s. 5K, I guess you don't consider Esaki to be kaiseki. I think they refer to themselves as contemporary kaiseki.