For Rico, I think her chances of becoming iconic in one fashion or another would be greatly increased if she does, in fact, turn out to be Ash's daughter. I also think the amount of time she stays will be determined by whether or not she is related to Ash or not. If not, I can easily see her being replaced in Gen 10 if she's not Ash-levels of popular, which would be less likely if she's not Ash's daughter or related to him in some other familial way. If she is Ash's daughter, though, I can see her staying for quite a while, and her popularity would likely be greater as well, as long as the Pokémon writers make her at least somewhat likable, which should not be too difficult.
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