In Esperanto, why does ĉiu mean "every" when ĉi serves elsewhere as a proximal prefix (e.g. ĉi-flanke) and -u is a suffix meaning "one"? Why does this not mean "this one" just as ti+ -u means "that one"?
No, for the correlatives holds:
ĉi-, ki-, ti-, neni-, i- and
-el and such are not independent parts, roots, and have nothing to do with roots
ĉi or imperative verb suffix
The definition of -u is adjective selection of one of some, with persons used as noun.
The definition of ĉi- is all/every.
The correlatives "happen" to form a table with similarities. In fact this holds for natural languages too, to some degree.
ki- the indoeuropean Q: q (Italian) / k (Russian) / w (German).
what, who, which, where. The same for
that, there, this.
Mind that this table of 5 x 9 is more elaborate than most languages, and not every entry has the same frequency, even
ki- serve different cases
-u for persons too;
ki- for both questions and subsentences. Linguists sometimes find this not a positive feature of Esperanto, though IMHO natural languages provide the foundation.
Ido removed the table.
And of course on may say
ĉiuj ĉi, ĉi ĉiuj = all these ĉial ĉi = for all these reasons tiu ĉi = this