Making food fancy...
As others said, the idea is to "refine" the sauce. By straining it, you refine it.
This all came about because
Smooth = elegant (requires more time, equipment, labor, signifying wealth).
Chunky = Rustic (peasant food).
I was in a class for creating healthier versions of fat-laden favorites. The instructor had an assistant from the local culinary academy, who of course is trained in the classic tradition.
The assistant was asked to prep some tomatoes for a dish, and she started off doing it as they do in school, peeling the tomato, deseeding, removing all of the jucies, and leaving just the actual tomato flesh to go into the recipe.
The instructor screamed: "What are you doing? You're killing the tomatoes!" She of course wanted all of those nutrients in her dish that the student was removing.