Wonder Woman is a character designed to force people into compliance through dominance.
That is truth, from the words of Dr Marston himself. Before we go any further, if you don't like that, you don't like an underlying principle of the character (which is fine, I don't intend to come across *****e-y) and can disregard the rest of the post.
Now, the dominance can arise in two ways. Physical manipulation (the generic warrior incarnation) or psychological (Marston's).
He chose psychological, specifically sexual, a woman who would tie up her enemies, and have a rope that compels them to do as she says. That can connote to sexual means, despite being a physical act. Now, it's not actually sexual, but it preys on the mind, it looks sexual, therefore psychologically, rewarding, men almost want to be defeated by her. But the real reward is rehabilitation (not killing or maiming) of said foe, and rather learning compassion for those they wronged. Hence why Wonder Woman's foes are largely straight women, a lot of the tactics from Themyscira are useless on them, they as women (or the more sensible gender), already understand her, they just disagree.
The relic you speak of is why the Amazons exist, the Lasso, the iconography (I know you don't like it). In short, it IS Wonder Woman in the same way Batman is a dark avenger. It's like asking why Batman "needs" to be dark when, he doesn't, he just is.
If I might ask, how would you "modernise" the core of her character?
Then they are missing the point. Exact same, no, no character has been the exact same. But similar, I'd see it.