6 pages... it MUST have been mentioned by now...
Real musicians use a system of writing music better known as notation. It involves five lines with dots and funny symbols on and between the lines. Ar the start of the notation they use funny symbols that indicate to the musicians what key to play in.
Sometimes they use flats, sometimes sharps.
Try writing the key signature for A Sharp of C Sharp, for example, and you'll see why they're always written as B Flat and D Flat.
That was my point earlier. Technically, there is no key of A# major, it doesn't exist because it's not in the order of sharps, so it has to be Bb major.
The keys of C# major and Db major are both fair game and it's incorrect to say that Db is always used. "More commonly," is likely more accurate. Bach's BWV848 is in C# major for example; you can't really argue against the technical merits of Bach's work.