Answer: Glad you enjoy the page.

The historical approach helps in questions like this, because systems as elaborate as modern music don't arise fully formed. They start small. In the beginning was the sung pitch, and the pitch was neither sharp nor flat. There was just singing, and the singing tended to fall into patterns of whole and half steps that would fill in the space between obvious acoustical stopping points like the fifth and the octave. Theorists worked out scientific explanations for the stopping points, which had a certain mathematical beauty, and thus were born what eventually turned into regular "modes," patterns like whole step, half step, whole step, whole step, etc.

But still no sharps or flats. Early writers did assign Roman letters to the pitches, and "A" was adopted as the beginning of the pattern that today we call the natural minor scale when carried out to the octave. And if you keep the same pattern but begin on its third note, C, you get what now would be called a major scale. Of course, no one had ever thought in terms of those modern scales; in the 11th century Guido of Arezzo taught his students to sing with a pattern of steps called the "hexachord:" whole step, whole step, half step, whole step, whole step. This pattern could be sung starting on G or C using only natural notes, and it's the origin of our do, re, mi, fa, sol, la.

Sharps and flats were not needed at all unless you wanted to start a hexachord on, say, F. Then you needed a lower form of B that would make a half step up from A. Thus was born "b flat" as distinguished from "b natural," and the signs used to indicate that difference between a lower and higher form of B eventually developed into our signs for flat, natural, and sharp. Those three hexachords on G, C, and F were enough to cover the ground, until the desire arose for further transpositions and more added half steps.

That's a roundabout way of getting to where I can say that if you began a major scale pattern on the note A, you'd have to put in sharps because the original scale on A was not like our modern major, but corresponded to modern minor. Wasn't planned that way; it just grew naturally.