If you look at the Ä page, you’ll see that not always Ä is a replacement for Æ (or ae), and it is still used in various languages.
The letter ß instead:
While the letter “ß” has been used in other languages, it is now only used in German. However, it is not used in Switzerland, Liechtenstein or Namibia.[1] German speakers in Germany, Austria, Belgium,[2] Denmark,[3] Luxembourg[4] and South Tyrol, Italy[5] follow the standard rules for ß.
So the ß is used in a single language, with a single rule (ß == ss), while the Ä is used in multiple languages with multiple rules.
Note that, considering that case folding is:
Case folding is primarily used for caseless comparison of text, such as identifiers in a computer program, rather than actual text transformation
The official Unicode 7.0 Case Folding Properties tells us that
00DF; F; 0073 0073; # LATIN SMALL LETTER SHARP S
where 00DF is ß and 0073 is s, so ß can be considered, for caseless comparison, as ss.