Exactly and ä is never just a, ö never just o and ü never just u. Words like "Uber" just feel wrong from a German perspective.
Also, ß is ss and since words don't start with Ss there is no need for an uppercase ß. When whole words are capitalized ß turns into SS.
Of course there is a little edge case where capitalization isn't reversible. For example, is the capitalized version of the name
MASSMANN to be converted to Maßmann or Massmann?
That is in my opinion the only reason the uppercase ß was added to Unicode. To resolve this ambiguity. It has no place in proper German typography.
