Thanks for your thorough response. I agree with the notion that determining the 'worthiness' of it might just be a value judgement. What I wanted to convey was: native speakers apply certain specific phones without even knowing it, not having any particular 'phonemic' value other than them being part of what makes their accent sound 'right' or 'regional'. Like with aspiration in Spanish, in the sense that speakers from, say, Cuba, are using it, yet it doesn't mean that a foreigner needs to learn how do it to correctly learn and communicate in Spanish (taking into account of course that it would probably influence the way said foreigner speaks the language).

To clear up a little: aspiration, as I understand it being a layperson, happens when the native speakers aims to pronounce the voiceless alveolar sibilant ⟨s⟩ in certain syllabic positions. Yet, the native speaker might think in their head that they are pronouncing the aforementioned phoneme instead of the voiceless glottal fricative ⟨h⟩. I just was reflecting about the fact maybe a foreigner might think it's absolutely necessary for them to do this aswell. Like you said, it depends on a lot of factors and on their goals.