There is, but it also has an additional trust layer on top, where you have to trust you're getting back responses from the models you're being sold and aren't being artificially quantised or stealthily redirected to cheaper models.

I trust ( although some don't ), Anthropic not to be doing that. I don't trust intermediate providers so much. If you're self-hosting then at least you know exactly what is running and get privacy on top.

Likewise you lose privacy of local hosting, and if it emerged that a provider was training on data they shouldn't be, would you have the necessary legal recourse, that you would going direct to the major model providers?