I think the swordmage/gish has a pretty strong identity, actually. It’s more like the fighter than like the paladin, in that each archetype is an archetype, whereas paladin is the archetype and the subclasses are variations of that archetype.
What I mean is, the identity is “warrior whose traditions are both martial and arcane”, with the single most important aspect being that the character doesn’t feel like a multiclass.
EK isn’t a good gish because it very strongly feels like a fighter who learned some spells in an exchange program. An actual gish should feel like a graduate from a school where you learn spells with sword in hand, and the sparring ring hums with magic, because the two elements are not separate in any way.