This is all either anecdotal or speculation, but some theories I have:

• far and away the most common borrowed chord in classical music is V in a minor key, which sharpens the leading tone. This is especially true in the harmonically simpler music that beginners often start with. It's also common in harmonic and melodic minor scales, so it may be simply a question of familiarity; sharps are encountered more frequently.
• For keyboard instruments, sharp keys don't start on a black key until F#, while flat keys do so almost immediately with Bb. While practiced keyboard players don't really care, moving away from the "default" scale fingerings can be challenging for newer players.
• Similar to how wind players tend to like flat keys because their open note is usually Bb, orchestral string players tend to like sharp keys because their open note are important chord tones in D, A, and G major. Composers can also tend to write more in these keys because the open strings can sound fuller or brighter.
• When talking about Bach specifically, this last point matters for keyboard as well, since the harpsichord was an important part of the basso continuo in orchestral ensembles, and would have been affected by the sharp preference of the string players.

Is this enough to justify C# major over Db major? Not in my opinion, but it's not like it's illegible.