(That the Geneva Protocol of 1925 outlawed chemical agents in war and was signed by all the European participants in World War II does not itself explain the non-use of gas; it only provided an agreement that both sides could keep if they chose to, under pain of reciprocity.)

Not only.

Past the very start, there were simple practical limitations. Chemical weapons in conventional warfare as understood at the time were both very limited and very circumstantial.

1. The point of using chemical munitions (per Soviet artillery manual from 1930s) was not to inflict casualties, but to inflict inconvenience of working in a gas mask. This, of course, in particular weakens the enemy capabilities that require both quick and accurate action: AA and counter-battery fire. That’s something one would want to do before an attack… in a very limited window of opportunity, and if the weather is favorable at all.

2. Put yourself in the boots of the commander of some Soviet artillery regiment. Given a choice, would you request:

A: one crate of gas shells which gives you an edge severely contingent on the circumstances (see above), and create extra risks if the enemy hits your ammo dump; or

B: one more crate of HE shells, which will certainly come useful. Or maybe AP, if there’s much armor on this part of the front.

It’s a no-brainer. And if no one in the whole division asks for chemical shells, the division does not want them, and then they will not be available anyway.
The same considerations apply to a German commander, who may also deal with shortages more often. In which case one just cannot afford carrying ammunition that may not be useful. And that’s if chemical shells were produced for his weapons at all.
The Americans and Brits would have to carry ammunition by ships (some of which may be sunk, creating random shortages), not just send a telegram for what to load on the next train. Do not want.

3. Meanwhile, the ammunition factories have enough of trouble simply excreting TNT into metal jars as fast as they can. Oh, and after mobilization most workers are hastily trained replacements. The industry is understandably reluctant to make anything too fancy or hazardous in handling, unless really, really necessary.

So both supply and demand exhibit consistent aversion to this product, and it’s de-prioritized into oblivion.

Just as business firms may “negotiate” an understanding that they will compete by advertising but not by price cuts, and rival candidates may agree implicitly to attack each other’s policies but not their private lives; as street gangs may “agree” to fight with fists and stones but not knives or guns and not to call in outside help; military commanders may agree to accept prisoners of war, and nations may agree to accept limitations on the forces they will commit or the targets they will destroy.

Comment: Most military commanders probably still have some notions of honor in most countries. However, a sufficiently fanatical warfighter might publicly claim to fight a limited war while promoting war crimes out of a private desire for total war. The world has few “total war” leaders comparable to Genghis Khan, but the world has too many secret sadists like Che Guevara and slippery militants like Jabotinsky.

Just as a strike or a price war or a racketeer’s stink bomb in a restaurant is part of the bargaining and not a separate activity conducted for its own sake, a way of making threats and exerting pressure, so was the war in Korea a “negotiation” over the political status of that country.

When dealing with narcissists and unhinged, unethical businesspersons, sometimes I think the stink bombs in public are more an expression of personal criminal insanity than rational-but-unethical racketeering strategy.

Much of this bargaining is tacit. Communication is by deed rather than by word, and the understandings are not enforceable except by some threat of reciprocity, retaliation, or the breakdown of all restraint.

I believe it was Colonel David Hackworth who said that the battlefield is the most honest place on earth. That may be why honest soldiers develop a particular sense of honor after fighting on battlefields. In civilian life, unfortunately, the lack of honesty and civility is the kind of thing R. E. Howard would have noted with comments like: “Civilized men are more discourteous than savages because they know they can be impolite without having their skulls split, as a general thing.”