I like what I call the disambiguation theory for why we have such odd words and spellings of words in English. Often times the best explanation of “why” we use a particular word or spelling is because the alternatives would be ambiguous. And in the case of Open/Closed you are describing a binary situation, the opposite of ambiguity, so there is pressure linguistically speaking to be crystal clear.
‘Close’ is ambiguous because it can be interpreted as a command verb, an adjective, or a noun, and it has a variety of meanings some of which can be confusing. In old English, they did actually say ‘close’ to mean ‘closed’. But a sign that said “close’ for example could be interpreted as meaning you were close to where you wanted to be, or just a command to keep a door closed for example, and not the state of the store.
“Open” has a number of meanings but they I think they all work for a door sign. Also the concept of being open is that of an ongoing state. If you say “opened” it moves the state into the past. It was opened, but is it still?
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