I've read the 4th amendment as a limitation on what can be done without a warrant, not with a warrant. But reflecting on what you wrote, and re-reading the 4th

I've read the 4th amendment as a limitation on what can be done without a warrant, not with a warrant. But reflecting on what you wrote, and re-reading the 4th amendment, you are right, that having a warrant doesn't mean a search is automatically reasonable.