Magneto made it clear at the end of First Class that he wanted a telepath on his team and in his life. So it does beg the question of what became of Ms Frost. I doubt we'll get the answer, though. And I doubt we'll see any more of Ms Frost to be honest. Doesn't mean it's not a shame.
I'm not sure if we'll get an answer. Singer was good about connecting the dots and addressing X-Men's loose ends with a line or two in X2. We'll see if he does the same in Days of Future Past. Though, after an 11 year gap, it might be strange that Magneto is still hung up on past Brotherhood members. We'll see.
Frost has had some great moments in the comics. The shifting allegiances, the battle with Phoenix, joining the X-Men, teaching Iceman how to expand his abilities, switching minds with Storm (where she sees how Storm perceives the world and its elements), not to mention the sarcastic attitude. It is a pity all that has gone down the drain on screen.
She does have great moments in the comics. Unfortunately, I think a lot of the moments you listed were lost even before First Class. Emma's interesting dynamics, in my opinion, lie in her history with the Hellfire Club and how her villainous background later affects her relationships with the X-Men, particularly Iceman, Kitty Pryde, and Storm, but more notably Cyclops and Jean Grey. All of that was seemingly lost when she was dropped from X-Men 3, and Fox decided that The Last Stand would be "the last X-Men movie ever."
As for X-Men Origins, I can't be clear enough how glad I am they ditched that version of the character, as Emma most likely would have been little more than a feisty blonde interested in Cyclops.
http://www.youtube.com/watch?v=TDY5T1nSBys
Emma Frost, known for her trademark white and formerly known as the White Queen, in a black leather jacket? Really?
I thought as much, which is why I don't really understand why Theron's role in Prometheus is an indicator that she'd make a good Emma Frost. That character was so dour and humourless.
To be fair, there is a bit of a dividing line between Emma Frost, The Hellfire Club's White Queen, and the Emma Frost of today, who is far better developed and less one note. It's really only after the X-Men movies debuted, that she became such a prominent character in the main X-Books. Still, she's never been as sullen as Theron's Vickers in Prometheus.