I haven't played with Surgical Extraction yet, but what you wrote here sounds right to me. It's tempting to sit back and imagine all the possible excellent uses for a card like SE, but this kind of wishful mindset can be alluring and dangerous. We have to keep in mind the damage we do ourselves when siding in more than the minimum number of cards. Part of what makes our deck powerful is that nearly every card functions as a terrific threat. Our most lowly 1/1s threaten to break most games wide open thanks to their synergies with virtually everything we play. I'd usually rather top-deck a dork than a Surgical Extraction. And if the idea is that I should mulligan until I've got Extraction in hand as an answer to, say, Reanimator, well, I'd rather just play the uncounterable Faerie Macabre. As an answer to other kinds of decks, SE seems rather impotent.
I admit that Surgical Extraction is hard to play properly so maybe I'm just ignorant of its best-use cases. Depending on meta needs, I feel either (1) a dedicated hand-picky or (2) a dedicated graveyard hate card would be better. If SE were in my board, I really don't know when I'd board it in, since presumably I would have already boarded in some Cabal Therapies before it, and anything beyond that just weakens our deck.
It just seems like a card that needs countermagic alongside it to function best. E.g. "I counter your spell, and now I SE it for two life" seems a lot better than "I watch your spell resolve—but hey, don't do it again!"
Also, thanks so much for the new primer, danyul.