The answer lies in the paragraph you so eloquently quoted: “ASKED SCRIMGEOUR”. Hermione was obviously just trying to present her opinion of the then current politics and the world situation and the Ministry’s incompetence.
Apparently, our Great Author has decided (and she can, because she wrote the books!) that after the fall of the Death Eaters, when Kingsley Shacklebolt became the Minister for Magic (etc. etc), the world became a happier, better place with no dirty politics (oxymoron?), and Hermione now felt that her place was there.
Alternatively, Hermione stopped being one of those who followed authority and complained about it, and rather became a person who “took the law into her own hands”, and decided that a way to MAKE the world a better place would be by becoming a politician herself. That would mean that she wasn’t “following a career in Magical Law”, but rather using that as a platform to fulfill her dream career.
But good point anyway!