I would disagree. Having all the messages locally and sending them with the request means you can switch inference providers or even models mid-conversation. It also means that the provider doesn't store the entire context, which often contains massive parts of proprietary codebases, secrets and PII and instead the agent harness manages all that.
While a simple `continue thread` API field might seem more convenient, the cost is still determined by the input token count and cache rate, so it just abstracts this crucial implementation detail away.