What does having or not having a visa do from a TSA perspective? They have zero input into your immigration status, they just need to match some form of government photo ID to your boarding pass.

Point being, you don't need to show your passport to TSA unless it's the only form of photo ID that you have that the clerk feels like accepting that day. If you do need to show your passport, all you need to be concerned about is that the name and photo match your mug and the name on the boarding pass. You could be an illegal immigrant with a 5-year old tourist visa, that's irrelevant to getting on the plane.