Both are powerful politicians, channelers, come from the same culture and seem to have a similar attitude towards many things. Besides that, Elayne is already the mother of Rand's children and seems the most similar to Ilyena, LTT's "soulmate", so to speak.

Min isn't a channeler and thus wouldn't live as long as Rand. She also seems too obsessed with Rand. Aviendha is too stuck in her - for Wetlanders often strange - Aiel mindset.