"Simple is best" is probably the phrase you want to use.
Compare to an adage like "mother knows best." The phrase is idiomatic - a token of speech that can't be divided - so "mother knows the best" sounds wrong.
It's harder to pin down the reason for this. In the first case, the phrase means that the simplest way is the best way. In the second case, your mother knows the best thing to do. These statements became shortened over time.
The meter of speech has a lot to do with the way idioms evolve. Words are dropped, and ungrammatical phrases may result. In this case, the idiom prescribes the grammar, not the other way around, so I don't think it's fruitful to speak of whether "best" is being used as an adjective or a noun.
Theodore Bernstein says in The Careful Writer: "A writer tampers with idiom at his own peril, and the peril is great. When he writes, 'At that time Sceptre was all except [two syllables] invisible in the haze,' he has flouted the idiom 'all but'."