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I've recently uncovered a mechanical secret that surgical extraction has been hiding from me for years.
I take my mill seriously and will go to many length to gain that extra edge.

In many versions of my mill, I have used chancellor of the Spires to be able to surgical extract an opponent before they even get past their first upkeep. That trick has won me many games, but there is a secret to it that I've never realised were there.

In my current mill deck, "stream of thought mill v7"
(Search for the tag: wdm mill guide)
I use lots of removal, and during test games I've been using paperstrips to keep track of how surgical extraction was performing.

I noticed that in some games it worked flawlessly, and in others it worked perfectly.
But as my deck has gained more and more removal, surgical extraction started to misbehave.

What was behind that degrading of its performance?

During one game I got struck by realisation. I was wondering on how the absence of mill could possibly worsen the performance of the damned card. After all I had the removal to throw the initial creature in the grave so surgical could step in and remove the rest.

The answer depends on the very nature of the mill cards you use.
Which of two following five cards do you think helps surgical extraction less ?

Archive trap
Chancellor of the spires
Glimpse the unthinkable
Shriekhorn
Tome scour

Have you thought about it ?

The shocking truth is the trap and the glimpse.

Why?

Because they take a little time before they mill something and during that gap in time your opponent gets to cast something that you could have removed by drawing one of the other cards.

This is why chancellor of the Spires works so well for me, and why I use stream of thought in the first place.
The changes in my deck towards more removal has also changed my behaviour. I used to play stream of thought at turn 1, but recently I've played it some turns later to be able to reshuffle removal cards.

The thing that makes surgical extraction good is when you mill a large enough portion of cards to increase the odds that the card you target happens to be a card that the opponent have in their hand as well.

What should I extract if for instance if i mill the following cards at turn 1 ?:
2 lord of Atlantis (gives other merfolk +1/+1) costs UU.
1 merrow rejereey (gives other merfolk +1/+1) costs UU.
1 æther vial.

You extract the merrow rejereey, because there is only 2 lord of Atlantis left in the deck or their hand, while there are three rejereey. Odds are simply higher that they have a rejereey in hand.

The conclusion is that surgical extraction has a higher chance of crippling a hand based on you milling as much as possible as fast as possible.

That's why chancellor of the Spires is so far the superior support card to surgical extraction (and extirpate)