What do you mean she doesn't have a power base? She has the BA hunters, two Blue Sitters, etc. as a solid support base in the Hall of the Tower. Together, they ensure that the Hall cannot pass any legislation that she strongly opposes. She also has Silviana, Nynaeve and Siuan, all influential women in the Tower.

Then, she has the position itself. As she showed with her actions to get the rulers of world to meet Rand, as long as you approach its power rationally, just being the Amyrlin Seat is a lot of power. Short of the Dragon Reborn, it is the most powerful position in the world, and that still holds true.

The reason why I think she isn't a great ruler is different. I think, like Rand, Nynaeve, Cadsuane, etc., Egwene is usually a quantum ahead of the people she's leading and is impatient at the slow speed with which they catch up. When she is concerned with the Seals, for example, many of those she leads are concerned with politics. She has not yet shown to ability to make a huge number of her followers excited about what she wants to do. She's spent too long having to manipulate them, and so she doesn't resort to simply talking to people like Romanda and Lelaine and trying to include them in her concerns.

People like Perrin, on the other hand, are better because they are blunt with the people they lead. Egwene needs that. Rand needed that, but has improved dramatically after his epiphany. Egwene may be headed there, but she has a ways to go yet.