>>Any amendments proposed by a convention still have to be ratified by 3/4'ths of the states. It's not a slam dunk that anything a convention drafts will be ratified.
Actually, I don't think that is clear. There has not been one since the first convention, and there was no question of its proposals being ratified, they had to be adopted. Since the convention is itself established by the states, there is a case for saying that, unlike proposals from Congress these would not need ratification by the states. There is simply no precedent, and I have no doubt the Supreme Court would ultimately have to rule on the status and powers of the convention.
What scares me is the thought of what a group of today's politicians would put into a constitution if starting from scratch (as is often proposed in the UK, where we do not have a written constitution). I fear that a "right" to things like education and healthcare would be in there.
There are two methods of proposing constitutional amendments and two methods for ratification. Congress can propose them with 2/3'ths vote in both the House and the Senate. The legislatures of 2/3'rds of the states can call for a constitutional convention which could draft amendments. Three-Fourths of the states can ratify amendments by a vote in their legislatures. Also 3/4'ths of the states can ratify by state constitutional conventions.
Only once has a constitutional amendment been ratified by state constitutional conventions. That was in 1933 with the 21'st amendment to repeal prohibition. Many state legislatures passed resolutions making a state-wide referendum to be a state constitutional convention.
Article V.The Congress, whenever two thirds of both Houses shall deem it necessary, shall propose Amendments to this Constitution, or, on the Application of the Legislatures of two thirds of the several States, shall call a Convention for proposing Amendments, which, in either Case, shall be valid to all Intents and Purposes, as part of this Constitution, when ratified by the Legislatures of three fourths of the several States, or by Conventions in three fourths thereof, as the one or the other Mode of Ratification may be proposed by the Congress; Provided that no Amendment which may be made prior to the Year One thousand eight hundred and eight shall in any Manner affect the first and fourth Clauses in the Ninth Section of the first Article; and that no State, without its Consent, shall be deprived of its equal Suffrage in the Senate.