A staff with a separate line or space for every semitone would probably be pretty unreadable, and the places corresponding to non-scale tones would go mostly unused in most music. Besides, the key signature at the start is very useful to any experienced musician as it immediately tells them how the piece is supposed to be played. You can think of it as a header that tells you how the rest of the notation should be interpreted.

I don't think it's a coincidence at all that the common Western staff has five lines and four spaces - it's a small enough number that subitizing [0] is possible. After all, the notation has evolved to be convenient to those who need to read or write sheet music, even though it might look weird to a layman.

[0] https://en.wikipedia.org/wiki/Subitizing