A wonderful website linked to me by @snailplane1 categorizes adjectives by their 39 different endings.
It notes that:
- 「エ段+い」で終わる形容詞は俗語を除いて存在しない。
- 「しい」で終わる形容詞は最も数が多い。
- 逆に「しい」を除けば、「イ段+い」で終わる形容詞は、ほとんど存在しない。
Though there are a number of interesting things suggested by this data, and the above observations, two in particular stand out:
- No adjectives ending
/ei/
exist outside of colloquial language... but they do exist in colloquial language.
- As you notes, aside from those adjectives ending in
/sii/
, there are very few adjectives ending in /ii/
... but some examples do exist.
Some archaic or colloquial examples offered are:
かいい、かそけい、さやけい、つゆけい、のどけい、はるけい、むくつけい、しんきい、すきずきい、つきづきい、あまねい、いぶせい、いみい、なめい、しげい
I don't claim to know what these words mean or how they are/were used, however.
Now, "why" is a very difficult question to answer, but the fact that these words do exist in archaic and colloquial speech suggests that there is more to this situation. I hypothesize that the reason these largely don't exist in standard Japanese is a uniform sound change that occurred in the past (though I don't know the details of said sound change).
In my experience, many dialects of Japanese retain more archaic forms (though this is probably not universally true), so that may explain why some dialects have words ending in /ei/
.
The two remaining examples of adjectives ending in /ii/
are いい and 大きい... but both of these are a bit special. いい is an irregular form of よい, and 大きい has the odd form 大きな. While I can't say this with certainty, I suspect these irregularities have something to do with why they continue to exist in modern Japanese.
1 http://homepage3.nifty.com/jgrammar/ja/adjec001.htm