That’s because we say “The shop **is** open”, emphasising that it’s open to customers *right now*, but the verb “close” (as in “shut down”, not “near”) cannot be used in the same way, so instead we say “The shop **has been** closed”. Both “open” and “closed” can be used as adjectives (“open shop” and “closed shop”), so they still make sense on either side of a sign.
For a time English was somewhat isolated and it lost common features of Indo-European languages which modify the start/end of a word. Or those features were diminished. E.g. German words are often long because they stack endings that turns one word type (noun, verb, adjective) into another or change the meaning slightly. One way to still do that in English is using the past participle to turn a verb into an adjective.
Further English words can have pretty board definitions. As in they encompass what non-native speakers perceive as multiple concepts. So to differentiate between two meanings at some point it became convention to use the adjective “close” to mean “near” and turn “to close” into “closed” to mean “shut”.
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?
Each word kind of has an “origional” form (noun, verb, adjective, etc.) and when we want to use the word in a different form, we make changes to it. When we use it in the origional form, we don’t change it.
Close is originally a verb, so we make a change to it when we use it as an adjective — in this case, we use the past tense of the verb to turn it into an adjective.
Open is originally an adjective, so we don’t really need to make changes to it when we use it as an adjective.
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