I think browsers should require sites to request access to WebGPU like they do location and camera.
If a random webpage is asking to use my GPU (especially if it's a sketchy-looking site I just got redirected to), that would raise flags and I'd deny access. If a game or visualization requests access, especially if it's something I've heard others praise, I'd take the risk.
Sure, someone could embed a vulnerability in some decent app which uses the GPU for actual rendering, but it's a lot harder.