This is why the Constitution specifies a different qualification for those seeking the presidency:
Article II; Section I, U.S.Constitution: (Paragraph 5) No person except a natural born Citizen,or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty-five Years, and been fourteen Years a Resident within the United States.
All other Federal offices did not have this requirement..only the Presidency. That was because the Framers did not want someone whose parents had not been citizens leading this country in a time of war...... particularly against the Nation of whom the parents had been citizens. This would have been a major stumbling block so they wrote into the Constitution that phrase.... knowing that eventually there would be ample candidates whose parents had never been citizens of another Nation.
Many early seekers to the Presidency had at one earlier time been British Subjects, and this phrase allowed them to qualify early on. But eventually..... as time passed.... there were no more folks old enough to at one time have been British subjects.
The Presidency is the only Federal office with this requirement. You can be a Senator, a Representative, a Governor and even a Supreme Court Justice with Parents who had been (or are) foreign Nationals......but not the Presidency.
The Congress does not have the power to change Constitutional law by legislation.....only by convention.
You are incorrect.
The Constitution specifically enumerates the exclusive and unfettered power upon Congress. See Article I, Section 8, Clause 4. The phrase "To establish an uniform Rule of Naturalization, ..." means that ALL rules. Those that need a process to be naturalized, as well as the procedure for such naturalization and those that a citizens at birth (natural born citizens). Thus by saying who is and is not a citizen at birth, Congress is FULFILLING their power under the Constitution.
Further the 14th amendment confers citizenship at birth (i.e without the requirement of naturalization) upon those born on US soil and subject to it's jurisdiction.