Why haven't the defenders of Winterfell, in S8 of GOT, at least contemplated using wildfire to defend the castle (and humanity)?

I just watched 8.2. The defenders of Winterfell have been armed with Dragonglass and Valyrian steel as much as possible. But no-one has brought up wildfire. Why?

We know regular fire is effective against the walking dead. We know wildfire is pretty useful when defending a keep.
Tyrion has used it, sers Davos and Clegane have seen it being used, Cercei has used it. So why don't they at least fill some of the frozen trenches with it, instead of pointed sticks?

The simple answer of why the North doesn't use Wildfire to help defend Winterfell is because they don't have any. The only ones who know how to make it are the remaining pyromancers that are in King's Landing, Tyrion enlisted them to produce more for the battle of Blackwater Bay but he never knew how to make it himself.

Too dangerous.

As we know, Wildfire is extremely dangerous.

“There will be no mishaps, my lord Hand. The substance is prepared by
trained acolytes in a series of bare stone cells, and each jar is
removed by an apprentice and carried down here the instant it is
ready. Above each work cell is a room filled entirely with sand. A
protective spell has been laid on the floors, hmmm, most powerful. Any
fire in the cell below causes the floors to fall away, and the sand
smothers the blaze at once.”

Now imagine transporting it all the way there, across bumpy roads or anything of the like could spark it and then Boom, your wildfire is gone and so are a few of your soldiers.

Why haven't the defenders of Winterfell, in S8 of GOT, at least contemplated using wildfire to defend the castle (and humanity)?

For several reasons:

1. The only people who know how to make wildfire are the pyromancers of the Alchemists' Guild in King's Landing, and they are under the control / at the service of Cersie.


2. Even if the North could make wildfire, they probably wouldn't have enough time to make a worthwhile amount to use against 100,000+ wights.


3. Using wildfire doesn't go well with close quarters combat, which is the prevailing combat style for the army of the North.


4. The North's main defense/strategy against the Night King's army is harvesting and manufacturing weapons made of dragon glass... a substance much easier to acquire, proven to be effective, able to be issued to every soldier, and is reusable.


5. There's no indication that the North even has the proper resources/ingredients/equipment to make wildfire.

Explanation:

1. As it stands, the Alchemists' Guild is under the directive of Queen Cersie. Excluding the fact that none of them [the Alchemists' Guild members] may even believe the White Walkers are real, and/or have the inclination to join the North's cause, IMO, there's very little chance they could successfully leave King's Landing without being detected.




2. The distance between The Wall and Winterfell traveling by foot is roughly 625 miles. With the Night King's army moving at a somewhat slow pace (say 2MPH) but never stopping, it would take them roughly two weeks to get to Winterfell. That being said, I have serious doubts that enough wildfire could be produced in that amount of time, not to mention subtracting the amount of time it took for the army of the North to fully assemble at Winterfell.




3. Wildfire is typically used from a distance, either through some kind of "trap" (e.g., how it was used against Stannis Baratheon) or by catapulting it from afar. With the wights having such large numbers, the use of catapults being somewhat slow (and the North having a limited number of them), and the wights being able to move so quickly, using wildfire wouldn't be so effective in the long run of the battle.




4. Jon and Daenary's had already committed to using dragon glass as the primary weapon against the Night King's army. Swords, daggers and arrows could be issued to each and every member of the North's army, whereas wildfire would only be used from a distance with catapults or in single-use bottles that could be thrown (keep in mind that wildfire highly combustible though so the chances of those bottles exploding just from bouncing around is pretty high).




5. It's never mentioned how wildfire is made, and there's also no indication that the North even has the proper resources to manufacture wildfire. I assume though that takes takes a good amount of equipment, ingredients, time and care, given that not many people know how to make it and that it's a highly combustible substance.