Why is it valid to say おいしそうだ but not おいしいようだ? Not in terms of grammar, but in terms of what is natural and what's not.
Why do I mostly see i-adjectives taking そう but not よう or みたい? Is there some logic behind it? Some difference in nuance?
If you are curiously seeing something and saying something subjectively based on your direct visual observation, you must use そうだ. If ようだ was used even though you're directly seeing something, it would sound like you're indifferent or trying to put aside your direct observation.
So while both are perfectly valid and grammatical, おいしいようだ is far less common in practice.
See my answer here, too: Difference between そうです、 ようです and らしいです.
As you may be aware, both are grammatical.
From 大辞泉, the relevant meanings of そうだ and ようだ are:
そうだ 動詞・助動詞などの連用形、形容詞・形容動詞などの語幹に付き、語幹が1音節の形容詞には「さそうだ」、また助動詞「たい」「ない」に付くときは「たそうだ」「なそうだ」の形をとる。様態の意を表す。…というようすだ。今にも…するようなようすだ。
ようだ (主に文末に用いて)不確かな、または婉曲 (えんきょく) な断定の意を表す。「この機械はどこも故障していないようだ」
(emphasis added)
Both may be translated to 'to seem' in English, but そうだ is about 様態=appearance, how it looks and ようだ makes a sentence indirect.
You see おいしそうだ more often mostly because that's what people say 'it looks tasty' more often.