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Kiss of Styx of course can only show up in the well if you're using Death Defiance (and it can appear even if you haven't popped a DD). If you're using Stubborn Defiance instead, it's replaced by Touch of Styx.
Aether Net can only appear if you have a Call boon, Flame Wheels Release can only appear in Elysium, Night Spindle can only appear once you've unlocked Companions, and Skeletal Lure can only appear once you have the Fishing Rod.
That means, at best, Kiss of Styx is one out of 21 possible items that can appear. This gives you a roughly 14.3% chance of getting Kiss of Styx each time you find or reroll a well.
Assuming, with decent luck on spawns and aggressive rerolling, you have an average of 12 wells per run, that gives you a roughly 84.3% chance of finding at least one Kiss of Styx per run. Those are pretty good odds, but it also means you have a roughly 15.73% chance of never seeing a single Kiss of Styx in any given run, which is also pretty good odds.
And again, that's the best-case scenario. Even setting aside Flame Wheels Release, if we assume Aether Net, Night Spindle, and Skeletal Lure are in the pool as well, that brings the odds of never seeing a Kiss of Styx up to just over 20%. That's a lot. Ask any D&D player how often they roll a 4 or lower on a d20 in any given session.
That said i think Charon only sell those recharges if you already have lost one. If it's not the case or you did already lost one always, my bad.