How do you go about using stylistic alternatives to swap out the entire font for italics in a single file? Is this even a good idea?
It is possible (just swap each and every character), but it does not sound like a good idea. Your poor users won't be able to select italic the usual way, only with using software that support stylistic sets. Changing some text containing italics in another font to yours won't change the italics to yours. And the italics variant will not show up in any font menu.
There is even a feature for this, 'ital', yet I have not heard of applications which support this feature if present in Latin-script fonts -- afaik Adobe defined it with CJK fonts in mind. So you would need to offer the same behavior in an 'ssXX' feature too, at least.
I consider it as a convenient way for fonts whose italic lowercase are accompanied by upright uppercase, and have used it for both Litteratra and the OpenType version of df Rialto.
Since not all applications support OpenType layout tables, it makes sense to provide a separate italic font too ...
Karsten: afaik Adobe defined it with CJK fonts in mind
Yes. It enables one to build an East Asian font with a relatively small Latin subset, for e.g. Japanese Romaji, without needing to duplicate the entire Asian glyph set in multiple fonts for different styles of Latin letters. The 'ital' feature is, I believe, supported in the Asian versions of Adobe applications.
I would say this feature is not only East Asian-specific but also CFF-specific. It solves a problem that, in TrueType, would be solved by making a TrueType Collection (TTC) font.