Because it's part of the German language: https://en.m.wikipedia.org/wiki/Capital_%E1%BA%9E
Fraktur had/has other such lower case ligatures (tz, ch, sch, ss (not ß) et al) but for some reason only ß survived into Latin script as a full fledged letter. I have a lot of old (mostly 20th century) books in Fraktur and they all use these ligatures more consistently than the Latin ligatures are used.
Some sort of orthographic device is needed - s between two vowels means the first vowel is long and the consonant is voiced, and ss between two vowels means the first vowel is short and the consonant is voiceless. So it's useful to have a different case for when the first vowel is long and the consonant is voiceless:
Busen /bu:zən/
Busse /busə/
Buße /buːsə/
Vowel length isn't predictable from spelling in cases of consonant clusters and other digraphs: Hand /hant/ vs. Mond /moːnt/, Bruch /brux/ vs. Buch /buːx/, etc. So ss could've been used for both - or sz, although there are some words spelled with sz as a sequence of s and z, like Szene /stseːnə/.