It's partly historical, sharps and flats weren't invented til long after the 7 letter name system was already in use. But it's also much, much easier, as diatonic scales have 7 notes in them, therefore using each of the letters ocne, with sharps or flats as modifiers, rather than each key using a different combination of letter names.

It also makes much more sense from the point of view of written music- if you had to have a separate space/ line on a stave for each of the 12 notes, it would be really hard to read.