There are several considerations with regard to near to.
Near the door and near to the door mean exactly the same thing. There is no usage that is advanced by attaching to to the word near. To, in this case, is an unnecessary word which neither helps nor hinders communication. This is similar to the common phrasing where are you at where at is a completely unnecessary and wasteful addition. Just as some dictionaries will define where are you at because it is used by a large number of people, so will they provide a definition of near to.
Nevertheless, style books routinely condemn throwing purposeless words into sentences. I couldn't find any style books that recommended near to. I did find one that specifically advised against near to. Of course, nearer to and nearest to are quite acceptable.
oald8.oxfordlearnersdictionaries.com ...."HELP: Near to is not usually used before the name of a place, person, festival, etc."
If you use what are you near to or where are you at, you will be understood. However, Duo has to make choices when programming the computer. If you feel that near to should be included in their library of translations, then you should report that there is a subgroup of English speakers who routinely use that construction. Similarly, people who believe where are you at is acceptable should take the same action with the same argument.
I could not find any French-English dictionary that defines près de as near to. Currently, Duo believes near to is not an appropriate translation of près de. Until enough people join you in attracting Duo's attention to this issue, you will just have to remember that Duo doesn't accept it.
The moon is in the sky is perfectly good usage in the U.S. too. But it isn't about whether you and the community to which you belong use the phrase on a regular basis.
The issue is what does près de translate to. French/English dictionaries translate preposition près de as near or close to. They translate adverb près de as nearly. They do not give near to as a standard English translation. Neither does Duo.
That is because attaching at to where are you at, all to you all, to to near to, is deliberately adding an English word to a translation of a French sentence that is not included in the original French.
You are insisting that Duo teach non-English speakers that près de means near to even though French/English dictionaries say that it does not translate to that in their view. The fact that other translations of entirely different languages used in historical documents stipulate near to as a translation of the original text has no bearing on French.
"Near to my wife" really doesn't sound to good to the ear (native English speaker). Would you ever say "Near to my dog?" No, I don't think so. I'm sorry, but it really sounds incorrect. I don't mean to criticize you, of course not. Just wanted to point it out. No hard feelings :)
The French don't do it because it's only one word in their language. It's two different words in English. You might hear people say "my woman" in English, but it's informal, it does not necessarily refer to one's wife, and in many cases it comes across as sexist where "ma femme" presumably would not.
"À côte de" means "beside" whereas "près" means "near" or "close to". While it's usually safe to assume that if you're beside something you are also close to it, these are not synonyms (especially since I wouldn't assume the converse--if you're close to something, you're not necessarily beside it).