Not narratively speaking. Padme is the personification of the Republic. Anakin is the personification of the Jedi Order. They and their relationship is a microcosm of what faces the galaxy as a whole.
Also that it'd be much less scandalous. As much of a problem a romantic relationship between a student and teacher is, it's an internal matter for the Order. Something they can resolve behind closed doors. But Jedi aren't supposed to play favorites, and being personally attached to one of the Republic's leaders creates a conflict of interest. That's why they were under so much pressure to keep it secret.
Anakin wouldn't fall to the dark side because Ahsoka died.
I know not, I only meant it in the sense of shipping, objectively for the story of course not, however Ahsoka and Anakin share so much screen time and are so close that I can't help but have that feeling, they seem to have a love more than brotherly in an environment as cold as the jedi in the middle of a war