>>1279275ä, ö, ü are a result of semi-predictable vowel mutations in German. They're just a, o, u but affected by a front vowel (i, e) attached to the root at the end. It's the same type of mutation that gave English foot-feet and mouse-mice. So historically it's natural that German doesn't treat them as different letters, because they're a different "quality" of vowel rather than a full thing, like á in Spanish, â in French, à in Italian or ā in Latin; ironically when languages that had similar vowels and were influenced by German, like the Scandinavian languages, adopted them, the processes were completely foreign to them, so they became separate letters in collation. Eventually the letters became more-or-less standard when translating the same sounds in languages outside Europe, because the Latin alphabet didn't have any way to represent them originally, and it's much more elegant than filling your language with digraphs
*cough*Korean*bloodcough*.
The sharp S has a history that's just as specific for German, and it was born from a special variant of S that was common around a couple centuries back but became defunct due to typewriting differences. It only indicates that the S is silent, but that it also doesn't make the bowel before it short (unlike ss would), so it didn't have an accepted capital variant until recently. Since all initial Ss in German are voiced, the only time you'll ever see it is in dialect transcription of those dialect that do have voiceless S word-initially.
