I can't really think of a good opportunity for using "ĉial" (for every reason) or "ĉiel" (by every possibility). I think they are pretty theoretical words, so I'm not sure whether it's even reasonable to teach them.
I suppose if Duolingo didn't try at all, people would complain about the asymmetry.
"Nenial" (for no reason) and "neniel" (in no way) are probably also pretty rare.
- Mi amas ŝin pro ŝia inteligento, afableco, kaj beleco. Mi amas ŝin ĉial! = I love her for her intelligence, kindness, and beauty. I love her for every reason!
- Nenial ni militu! = For no reason should we go to war!
- Neniel mi povas trovi postenon. = No matter how I try I can't find a job.
There's nothing wrong with not using ĉial - Zamenhof didn't seem to use it at all!
But how often do you say "well, in any case"? English "any" in positive clauses generally translate to ĉio-series words (and to io-series in negative clauses).
- Al kia restoracio vi volus iri?
- Mi ŝatas ĉian. (ne ŝatas ian)
"Ĉiaokaze," as we know, means "in any event" and is very common. PIV defines "ĉial" "Pro ĉia motivo, ĉia kaŭzo."
PAG notes only that "ĉial" went unused by Z (and that it's also not in the universal dictionary). PMEG defines it as "pro ĉiuj" - which is a completely useless definition in practice. "Pro ĉia," though, is something someone might actually say.
Personally I wouldn't use it any anything formal because of the risk of confusion. But imagine a character saying "well, in any case" or "yeah, whatever." - nu ĉial; jes, ĉial
Ĉiel is extremely similar. Estu la vetero ĉiel. - Let the weather do as it will.
It's certainly difficult to translate this. Even in the Esperanto, it's questionable just what the exact meaning is. I have the feeling it means something along the lines of "for every possible reason". But even then, what exactly does that mean? It's not entirely clear, but it just emphasizes that there are many reasons for it!