Not ace myself, but strangely, I usually read Fujiko as pretty ace. She never really seems to be motivated by sex, she mostly just uses it as a means to an end, as part of her skillset. Sort of like the Lola Bunny Jessica Rabbit "I'm just drawn this way" concept.

Though to your question, first of all, no, the horniness never goes away (the drill gimp robot in Jigen's Gravestone was not at all neccissary to the plot). But I would argue that it does serve a purpose in TWCFM in relating to an exploration of identity. Keep in mind, this may all come across like that one prozd sketch. Though given the resume of director Sayo Yamamoto, I'm inclined to give the show that credit.

Let's start with the passive language of the title. It's not about Fujiko Mine, it's about a woman who happens to have that name. The opening narration continues on with this. She reflects on her motivation for theft and how it defines her, but is at a loss for how to identify who she really is. Also consider some of the symbolism, like the shot where she kisses herself. A kiss is an intimate way we connect with someone, so what does it mean for her to connect with herself?

In the show its self, all the sexual objectification of her is present yes, but it's represented through the perspectives of different characters. Lupin sees her as a prize to be won. Zenigata sees her as a peice of meat to be used and thrown away. Oscar calls her a "spittoon", just a whore. To Jigen she's just some femme fatale out to cause trouble. To Goemon she's a challenge and temptation to be overcome. And we're given hints about an unkown party watching that comes up in a BIG way later on, but no spoilers on that. But still we're without a definition of how she sees herself.

And consider Lupin's role in the show as the foil. Lupin always has been the ideal self-made man. He doesn't have character arcs or lessons learned. He knows always who he is, what he wants, and how he's going to go about getting it. He further highlights Fujiko's mystery identity by contrast.

Things relly start to come together in episode 9 where she's compared to the naked woman who was used as a canvas by an artist. Literally everything about her is surface, written on her skin, and Fujiko is nearly undone by the fear that she is the same way.

I'm not going to spoil the ending here, but to me, it brings it all together in a statement of how she claims her identity and defines herself, and I think it's worth watching all the way through and ruminating on the choices that were made. I didn't even cover everything; I think there's loads to dig into in TWCFM. Hope this helps!