I suspect her prominence played two roles.
One: yes, she's a woman. And regardless of what Tolkien/LOTR fans might do, it can be a worry to suits that women won't come to these sorts of movies. They might feel that having a woman on the poster suggests there is something in this story that might appeal to a woman.
Two: she was somewhat well known. Suits always feel more comfortable having actors people will recognize on their publicity products.
It was interesting to me that, for FOTR, the promotion involving music was very heavily focused on Enya. For the next two movies, the focus shifted more to the actual score and Howard Shore.
I suspect that they were using Enya to generate interest in the movie and back in that day, a singer like this involved with a movie would go on late night talk shows, etc. to perform the music and promote the movie.
As the movies generated their own steam, popularity and interest with fans, they didn't have to rely so heavily on *names*.
If you think about what might make you tune into a late night talk show, it will always be someone you recognize who is making the rounds to talk about their new project. It's rarely the unknown.
Also keep in mind, the people making the posters are rarely the actual filmmakers. I'm not sure how much veto or say they even have in the manner. The same with trailers.
So one really has to consider what someone in an office somewhere thinks will *sell* a movie. Someone perhaps totally disconnected from the actual project and/or fan base (or potential fan base).
Movie promotion is really different today than it was 1999-2003. Don't make any assumptions about why things were done 'then' by how they're done 'today' (not that you are, necessarily. I'm just not sure how old you were or how involved you were in the fandom in 1999-2003 such that you might remember.)