Why did they retain the diatonic system?

http://www.andymilne.dial.pipex.com/Scales.shtml
http://www.andymilne.dial.pipex.com/Diatonic.shtml

It's like the english language: people never fixed the phonetics because they were too lazy. Well, Webster came out with a phonetic dictionary after his current usage one, but everyone had bought that one already...
LAZY.

I'm not exactly sure what you're getting at with some of your other questions.

X mode in Y key is just A mode in B key. Why have two names?

Could you give an example of what you mean by this?

More than the staffs, the names of the notes. Why not just go to L?

Going out on a limb here...

First, there weren't 12 different notes used in medieval music. Second, enharmonically equivalent notes have only been interchangeable since equal temperament, and in commong practice theory they mean different things. Writing a C# can indicate an expected resolution to D, while Db will resolve to C. A performer on an instrument without fixed pitch may still perform them differently as well.

You take that diatonic system and transpose it a semitone and the idea of it being simplified based around a scale goes to hell.
That scale, even in another mode is not full of the sharps and/or flats that it avoided.
What of bebop scales, or the spanish 8 tone?

I don't follow what you're saying here at all.

The history of musical tuning and scales is convoluted, but the system continues to be used because it works well, particularly for music with functional harmony.

There's no rule that says bebop/8-note scales aren't allowed. There are accidentals all over the place in sheet music. And besides just being convention, having 7 names for notes is simply easier for people to wrap their heads around than 12.

The (modern, simplified) modal system is a bit silly, too.
X mode in Y key is just A mode in B key. Why have two names?

I like modes ;_;

But I think the more significant point is that gzeus wants to simplify things by using a single name for enharmonic pitches (e.g. using A-L means only 12 different names for pitches, which would eliminate enharmonics), but the fact is that enharmonic pitches are not simply interchangeable.

Music is a language, and languages, especially their written forms, are often convoluted. *shrug*

We know when Webster came out with his two dictionaries, but I've never heard of any competing systems.

I'm often REALLY inarticulate.
Sorry.

History of notation of accidentals

The three principal symbols indicating whether a note should be raised or lowered in pitch are derived from variations of the letter B: the sharp and natural signs from the square "B quadratum", and the flat sign from the round "B rotundum".

In the early days of European music notation (4-line staff Gregorian chant manuscripts), only the note B could be altered (i.e. have an accidental applied to it): it could be flattened, thus moving from the hexachordum durum (i.e. the hard hexachord: G-A-B-C-D-E) where it is natural, to the hexachordum molle (i.e. the soft hexachord: F-G-A-B♭-C-D) where it is flat; the note B is not present in the third hexachord hexachordum naturale (i.e. the natural hexachord: C-D-E-F-G-A).

This long use of B as the only altered note incidentally helps explain some notational peculiarities:

* the flat sign actually derives from a round B, signifying the B of the soft hexachord, that is, B flat (hence the name of the flat sign in French "bémol" from medieval French "bé mol" — modern French "bé mou" — or "soft b") and originally meant only B♭;
* the natural sign derives from a square B, signifying the B of the hard hexachord, that is, B natural (hence the name of the natural sign in French "bécarre" from medieval French "bé carre", earlier "bé quarre" — modern French "bé carré" — or "square b") and originally meant only B natural.

In the same way, in German music notation the letter B designates B flat while the letter H, which is actually a deformation of a square B, designates B natural.

As polyphony became more complex, notes other than B needed to be altered in order to avoid undesirable harmonic or melodic intervals (especially the augmented 4th, or tritone, that music theory writers referred to as "diabolus in musica", i.e. "the devil in music"). The first sharp in use was F♯, then came the second flat E♭, then C♯, G♯, etc.; by the 16th century B♭, E♭, A♭, D♭, G♭ and F♯, C♯, G♯, D♯ and A♯ were all in use to a greater or lesser extent.

However, those accidentals were often not notated in vocal part-books (but the correct pitches were always notated in tablature). The notational practice of not marking implied accidentals, leaving them to be supplied by the performer instead, was called musica ficta (i.e. "feigned music").

http://www.medieval.org/emfaq/harmony/tritone.html