Treaties are undemocratic by design. The framers worried that a democratic republic would not be able to present a unified front internationally. But the purpose of treaties was to govern international relations, not submarine domestic legislation under the guise of international relations.
Most treaties are CEA agreements that are subject to the presentment clause.
>>International treaties are given to the Senate on a take it or leave it basis,
Regular Treaties can certainly be amended by the senate that then makes ratification conditional.
>>and do not require any approval from the most democratic chamber of Congress: the House.
Hence the two thirds voting requirement for an international agreement that governs foreign relations.