On the one hand this is exactly the right solution to prevent lethal trifecta exfiltration attacks. The existence of lockdown mode does however imply that ChatGPT, in its default settings, does not provide robust protection against sufficiently determined data exfiltration attacks!
Looking at the trifecta axis, if we assume we can't control untrusted content, that leaves us to create safeguards for private data access and external communication.
Would it be enough if we had a buffer between when these two happened: access to the environment and access to the web?