This has always bothered me.

Why doesn't it play that familiar sound when Samus gets the Hyper Beam from the giant Baby metroid?

Would kind of take away from the immersion of it all don't you think? Not to mention cheapen the narrative Super Metroid had been crafting since first arriving on Ceres Station. First time playing through the game, after the baby gets blown away, it's a surprise to fire such a powerful beam and feels like satisfying revenge. Having the game pause during that to display "Hyper Beam" and play a fanfare would ruin the experience.

Besides its less of an item and more of a power transfer, acquired from Mother Brain through the Baby Metroid.

Thanks, I never thought about it before with respect to the surprise factor. Nor did I think of it as a power transfer from Mother Brain, until you mentioned it.