For inference, the best models are so large they won't fit in System RAM. GPT@home is not going to make a difference in that scenario.

For training such large models, data parallelism is no longer sufficient and tensor/pipeline parallelism is required. The problem is communication bottlenecks, differing device/network speeds and massive data transfer requirements become serious enough issues to kill any naive distributed training across the internet approach. Deep learning companies use fancy 100Gbps+ connections, do kernel hacking and use homogeneous hardware and it's still a serious challenge. There is no incentive for them to invest in something like GPT@home.

But it's not impossible and there's some research being done in the area. Although, it'll be a while until a GPT@home approach becomes a ready alternative. See https://arxiv.org/abs/2206.01288 and their recent GPT-JT test for more. Another development would be for networks to become more modular.