This is a problem that i'm actively working on (https://fudge.design), what i've realised is that it's simply not an issue of capability - given a well crafted site and a competently written visually aware harness, most recent models can replicate that website.

So it's what lies between saying "I want x website" -[.....] -> Code+Assets

The issue has to do with specification fidelity, in short a grill-me style aesthetic interrogation using illustrative tooling - ascii diagrams for specifying layout, copy and user-flow, image-gen mockups for higher fidelity mockups. References are also very important for nailing down the aesthetical qualities. I've noticed it's far better vs purely text description to simply gather up a mood-board telling the llm to find commonalities and come up with a design system and brand guide.

So I don't believe it's an unsolvable problem, it's simply a lack of effort on the implementors part. Also there's probably some survivor's bias here (you won't notice an intentionally designed vibe-coded site)

For example here's one reference exploration site i recently made with grok: https://explorer.withfudge.com/