==> Isn't there a problem with technically Ones and My not being true pronouns as they can not replace the object, as they are not a true determinent in a sentence.
There are several issues wrapped up in that question.
Determiners and pronouns are not the same thing. Determiners are always followed by nouns, whereas most pronouns usually are not followed by other nouns. "One" can be a pronoun, or "one" can be a determiner, but it can't be both at the same time. When "one" is possessive ("one's" - with an apostrohe 's'), then it's a determiner, and not a pronoun, and a noun will follow.
I'm not sure that "my" is ever a pronoun. "My" is almost always a possessive determiner, followed by a noun - whatever it is that is yours. The pronoun for that is "mine".
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