> The United States Congress does not really get line-item veto on giant international trade agreements that affect dozens of countries, all of whom also must ratify the treaty.

Its not a treaty. If it were a treaty, it would have to be ratified by a 2/3 vote in the Senate, and could, indeed, not be modified on a line-item level. What is put before Congress is a regular US law, not a treaty ratification, that needs a mere majority, but in both houses, and which just happens to be intended to implement an non-treaty agreement negotiated by the executive.

The US Congress does, really, have line-item authority over regular US laws.

> Trade promotion authority is simply the authorization for the administration to negotiate the treaty.

No, its not. Its a (without binding effect, since Constitutionally the Congress cannot bind its own future actions) commitment as to how Congress will apply its powers after such negotiations. The power to negotiate with foreign powers and submit whatever it wants to the Congress after such negotiations is inherent executive power that requires no authorization.