Has anyone actually made a legitimate alphabet key thingy?

[Mauro]

"s" too represents two different sounds ([s,z])

  But isn't there an algorithm that tells which is which, at least most of the time?  Like, single "s" sounds like [z] between vowels, like [ʃ] when combined with "ci" or "ce", like [s] otherwise?

and so does "z" ([ts,dz])

Isn't it [ts] only when doubled?  (Did I tell you about the import of "pizza" into Portuguese?)

There are some rules but they do not cover all the cases (and nobody knows them anyway). After putting in my software all the [s,z] rules I could find there are still words where [s] cannot be discriminated orthographically from [z]: in a typical text, about 4% of all word tokens. Same for "z", even if doubled, ie. 'razza' (race) is [rattsa] but 'razzo' (rocket) is usually [raddzo].

We do not differentiate much between the two sounds [s,z] (and [ts,dz], [e,ɛ], [o,ɔ], in many cases at least) and so the orthography reflects this, ie. collapsing [s,z] in the single glyph "s". Same for "z", "e" and "o". The problem is rather fundamental because the pronunciation changes from place to place, and I suspect it's always been so. Ie. 'casa' (house) is ['ka.za] in the North but ['ka.sa] in the South, 'neve' (snow) is ['ne.ve] in the North but ['nɛ.ve] in the South. For an Italian it's hard to tell the difference: any Italian who has not studied a little phonetics is completely unaware that there are two "e", [e] and [ɛ]. In the single case when this is relevant (distinguishing 'and' from 'is') what an Italian thinks is that [ɛ] is the stressed form of [e] (sic!). Ask a generic Italian and he'll tell you the language has 5 vowels, and he won't believe you if you tell him they are seven instead.