While they may sound the same, when defining intervals (used to construct any chord or scale) it is mandatory to specify using a sharp or flat.
For example:
Try to define a major third interval from C. You would come up with the note E, because it is two whole notes from C. Easy, right? You would never think of using Fb instead of E. An E is the third natural from C, and is therefor used to create any "third" interval.
Now let's make a minor third from C. Which is an Eb (E flat). There would be no reason of using a D# (D sharp) instead of Eb because it would define an augmented second. With the note D being the second natural from C.
Conclusion
While it is okay to name a note with a sharp or flat, when talking about a note in relation to an interval, chord, scale or even a music key, a more defined name must be used to keep music readable and understandable.
It's the musical equivalent of "hear" versus "here". Just because they are homophonic doesn't mean they are the same word. Similarly, in western tonal music B♭ doesn't mean the same as A♯.