It probably won't; the series doesn't really go into the mechanics of magic very much, but it does seem to have a semantic tie to their wish. Mami, for example, is canonically said to have her ribbon power because she wished to live. Because her wish reaffirms her 'ties to life', this is reflected by ribbons she can tie thing with.
Not that she actually used the words "tied to life" in her wish, according to the PSP. Which means the logic of the wish goes beyond the exact wording.
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