Indeed, that would have been a very good reason for styling herself by her husband's name, not hers -- notwithstanding the fact that she was a born princess (of another country). After all, she would have been forever confused with her unmarried sister-in-law, who happened also to be of the same age (born in 1850).
I learned that the "Mrs. Royals" system of titles actually originated in Germany; it later got copied by the British. Hence, Baroness Marie Christine von Reibnitz styling herself since 1978 as Princess Michael of Kent.
She probably would like to use her own personal names; but she has not reason to complain. After all, she got elevated from nobility to royalty at marriage, and received the letters HRH.
Similarly, Princess Theresa of Liechtenstein got elevated in her qualifying rank from Serene Highness to Royal Highness.