Yea I think being able not to leak is the bare minimum? But it really depends on how good it is at specific applications; I wouldn't give a tax-preparation agent my SSN unless I was confident that it was no more likely to misfile my taxes than a professional tax preparer.

In other words, the risk of harm doesn't need to be zero, just less than the equivalent risk of a human with similar skillset. So I'm comfortable riding in a waymo, and not comfortable giving chatgpt my SSN at this moment in time, but I expect that within 5-10 years (assuming no doom) I will trust some AI agent with my SSN because they will be better at handling sensitive info than humans

Then again, given the Equifax/Experian data breaches, your SSN is already out there and probably hoovered up as training data already