Godot has that potential, and can export to web. Though I do suspect LLMs have just come and taken that spot.

LLMs are not better at this than Godot, though agents can certainly use an engine.

The biggest problem is the Web has a dearth of good Flashy examples of people pouring their life into an experience, ever since the death of Flash. So web agents have no good training set for thinking creatively in this space.