I ocasionally hear sentences such as
髪が長くなりたい I want long hair
心が美しくありたい I want to have a beautiful heart
Although I might use similar constructions myself, I do not consider them fully correct because they sound like "(My/the) hair wants to become long" and "(My/the) heart wants to become beautiful". I am aware of Japanese "double-subject" sentences (although I don't agree with this term) and understand that these can be considered ～たい forms of them:
(私は)髪が長くなる → 髪が長くなりたい
(私は)心が美しい → 心が美しくありたい
but would prefer to rewrite to other forms:
Now my question is:
Are the first sentences I posted considered fully correct forms, or do others consider them slightly marked as well? I tried to google for some grammatic prescription related to this, but found it hard to know what to google for.
Edit after seeing answers:
So if 私は鼻が高くなりたい is grammatical, what is the common way to analyze this sentence?
Obviously, translating 高くなりたい as "want(s) to become high" doesn't work, since "I" is not the one wanting to become tall, and "nose" doesn't have a will of its own.
Is it that ～くなりたい operates on a phrase level, i.e.
私は(鼻が高)い I am tall-nosed
私は(鼻が高)くなりたい I want to be tall-nosed,
or is there another way to analyze this?