harry potter - Why doesn't either side in the Wizarding War use Felix Felicis?

I was thinking about an answer to an older question about HBP, and it dawned on me: merely getting a confirmation that there were 7 Horcruxes was important but hardly the most critical endeavour of the entire War (actually getting and destroying Horcruxs was). So why was Felix only used once, in that specific case?

We know Felix Felicis is hard to make, but we also know that it's possible to make. Slughorn can, for example.

Why doesn't either side in the War pay someone like Slughorn to make Felix for them?

A critical mission - like Dumbledore going to Gaunt shack, etc... - would be well worth the price no matter how expensive the potion is. And Slug likes his creature comforts, so he would be more than willing to put in the effort if paid well.

Hell, it is not so super priceless and rare and hard to make that Slug wasn't willing to give one as a prize to one of his students!

The obvious reasons don't seem to work:

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  Money is no object. Either side has wealthy wizards who can pay (Malfoy, Harry, Longbottom). For that matter, even if Dumbledore is not himself wealthy, he's a great enough wizard that he can trade some magical favors/inventions to Slughorn or another potion maker of his caliber.

  
  


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  Felix is not some deeply held secret. It's listed as prohibited aid for sporting events.

  
  


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  The fact that at the very least Slughorn is an advanced potion maker who can do it is also not exactly a secret - he told Harry's class he can make it, and probably told prior students of his (Tom Riddle included).

  
  


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  "... highly toxic in large quantities" answer from Slughorn from HBP. But there's a difference between frequent use/large quantities; and strategic rare use for critical missions (e.g. retrieving/destroying Horcruxes). Both Dumbledore and Voldemort possess enough willpower to enforce that (and DEs wouldn't even care too much in the first place)

  
  

I would strongly prefer canon based or JKR answers.

Answer

Well, there's always the consideration that Voldemort's side did use Felix Felicis at times. Canon doesn't indicate otherwise (and I realize that the absence of information does not a fact make). I think it's okay to consider the possibility that the Death Eaters engaged any and all methods of magic that might have given them an advantage, and it's fair to say that the Death Eaters had their fair share of successes and triumphs in their endeavors.

Felix Felicis is a tricky potion to brew and probably wouldn't be the best choice for mass production and consumption. In chapter 24 of Half-Blood Prince, Sectumsempra, Harry reads the instructions for Felix Felicis (which is indeed in the sixth year book Advanced Potion-Making, so there's no question that Snape would have known how to brew it) and notes that not only are the ingredients complex, but that it takes six months to brew Felix Felicis. War does not wait for a potion to finish brewing. Keeping Felix Felicis in supply, on demand, would have been incredibly difficult, if not impossible.

You already mentioned that Felix Felicis is toxic in high quantities. In Half-Blood Prince, chapter 9, The Half-Blood Prince, Slughorn mentions quite a few things about Felix Felicis. It's disastrous when brewed improperly. Slughorn doesn't mention how a potioneer would be able to tell if the potion wasn't brewed correctly, but if it's one of those situations where one wouldn't know until they take the potion, Felix Felicis would then be an incredibly risky potion to dole out to the troops on a regular basis.

Slughorn says Felix Felicis should be taken only sparingly and on occasion. Taking it too often causes giddiness, recklessness, and a false sense of overconfidence. He also says that this potion works from "dawn to dusk" -- what about any combat that takes place after dusk?¹

Naturally, Felix Felicis is an inherently abusable potion for those seeking the wonderful feelings of unstoppable confidence and accomplishment. In this regard, it would be at high risk for being regularly stolen by individuals looking to experience those particular feelings again and again.

Also, I think Felix Felicis gives the taker what they need, not what they want -- an important distinction. Harry needed Slughorn's memory of Tom Riddle. So bringing the topic back to a wartime situation, one person might want to kill another during a duel, but what they need is just to escape the situation alive, and Felix Felicis might facilitate escaping alive, but not the desire to take another's life.

¹_{This is actually contradicted in chapter 22 of Half-Blood Prince, After the Burial.}