I think the only reason Lanfear DIDN'T carve out a power base and start wreaking havoc was because she followed Rand. Mieron only became Forsaken because LTT spurned her love and married another woman. She waited 3,000 years for him, and when he came back he didn't remember that other woman, didn't remember spurning her, and maybe she could have another chance. She was never Forsaken just because she wanted the world to end or worshiped the DO.

So when she had her other chance, she went after him as Selande, then as herself, always offering her love, the world at his feet and her by his side. She went after Rand personally when all the other Forsaken bided their time and secured some power and defense against him. It was kinda ballsy, not really all that stupid. Plus, after she found out Rand's weakness for women, she pretty much figured she had him.

I think the biggest reason they renamed her Last Chance was because she was never really going after the Shadow's goals like she was supposed to. She went after Rand, failed to turn him to the Shadow or kill him, and she was trying to achieve her own "petty" goals the whole way.