As to the question of when to use はほしい [はほしい and not ほしくない]:
I think that @l'électeur gave one good example (=when emphasizing the contrast of what one wants and what not) with the example 「靴は欲しくないけど、ジーンズは欲しい。」
IF YOU READ FURTHER [NOT ADVISABLE, BUT I DON'T DELETE THIS
Due to the valuable comments
To indicate when は欲しい IS NOT USED ;-)
To call for additional case where は欲しい (and not e.g. が欲しい or は欲しくない) is used
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In addition I can think of at least two other situations to use は but at least I clicked on this question to find out more, so I hope the natives / gurus [also others than @l'électeur ] correct / add:
Can be used like in a [phrase or at least close] "あれはほしいこれはほしい" as a critical statement about someone with too many requests [and here it is more about requests than aspirations], i.e. in a stereotypical case two employees could talk about their boss [or similarly 2 managers could talk about someone's difficult team member] who is never satisfied and comes up with continues and unreasonable requests.
Can be used when the target of the aspirations is a bit abstract and/or not immediately achievable / obtainable, like I want that kind of life [ああ言う人生はほしい]