Here I can see your point, though honestly, if Egwene's guilty of that, most Aes Sedai other than Cadsuane, Moiraine and a few others are. Not being teenage girls, obviously, but self-involved and concerned with nothing but the Tower, their Ajah and themselves, not necessarily in that order.

Here, somewhat. Elayne has moments when her noble upbringing and lack of understanding of the real world shine through, but they're hardly that frequent, apart from the odd behaviour in SR and FoH; same with Egwene's occasional stupid ideas. And in later books, I don't think you can call either immature, much less inexperienced.

Actually, she's one of the smartest of the main characters. And, considering her upbringing, surprisingly good at admitting mistakes when she does get it wrong, as seen from Mat's PoV.

Gawyn as Anakin is funny because it's so true. As for Egwene and Padme, I haven't seen tPM in ages... but annoying as Egwene can be, and tiresome as her PoV gets, she's rarely naive.