Those cards, so familiar! Exactly what Opus produced for me.

Did Anthropic and/or OpenAI deliberately train their models to produce websites with a specific design language, or did these stylistic preferences emerge naturally as some kind of LLM-selected optimum?

It's not the base model, it's the system prompt in dev tools.

To give an example I'm personally frequently annoyed by, Google's Antigravity will consistently use the word "anthropomorphic" while "thinking" and the end result will consistently have obnoxiously large border radius (kind of like Android's design language).

Codex on the other hand likes to make websites with blue elements on a black background and likes to use emojis for icons for some reason, which is a terrible idea accessibility-wise.

AI has no taste, so I suspect the labs just gave it a bunch of decent looking boilerplate as preferred style.

When you bring your own ideas you can get AI to dev pretty nice looking non-generic stuff.