Updating weights means your changing this model.
To facilitate this feature, the inference provider would need to have your personalized model loaded into ram to process your request in a timely manner. Now multiply that by the number of users they're serving.
The amount of resources this would bind makes this infeasable for cloud inference like anthropic provides.
Also see LoRAX, it's an inference engine that exactly does this, it can serve many LoRas off a single base model
It is an interesting thought to explore. I admit I'm not a specialist whatsoever on the topic, from my perspective that sounds like an incredible challenging ops problem.... But again, I don't work for anthropic and maybe they're up to the challenge as you seem to think.
The crazy part is probably loading, running a model pr users - but if the untrained (unspecialized?) model can somehow stay resident - might be possible to load adjusted weights on demand?
I suppose each run now needs a different context pr user/customer anyway, for cache hit rate, if nothing else?