"I want xxx." vs. "I do not want xxx."
When you want something, you will generally say:
「XXX + が + ほしい」
and when you do not want something, you will generally say:
「XXX + は + ほしくない」
The only times you can and must use 「XXX + が + ほしくない」 is when it is used in the if-clause or relative clause. Thus, it is correct to say:
Relative Clause:「靴{くつ} + が * 欲{ほ}しくない人は靴屋{くつや}へは行かない。」
"A person who does not want shoes would not go to a shoestore."
If-Clause:「靴 + が + 欲しくなければ、なんで靴屋に来たの？」
"If you do not want shoes, why did you come to a shoestore?"
Moving on...
The contrastive 「は」
This is essentially a different topic from what has been discussed above.
It is correct to say:
「靴 + は + 欲しくない。」
when you do not want shoes but want another thing. Thus, you can say:
「靴は欲しくないけど、ジーンズは欲しい。」
That is a pair of contrasitive は's. "I don't want shoes, but I want some jeans."
I imagined that the reason is to make a contrast/comparison that は provide. Is that why?
No, as I stated above. We are talking about two different things. One is affirmative vs. negative. The other is contrastive.