If you don't know, a amendatory convention can be achieved by having two thirds of the state legislatures vote for one. If that happens then you must get a two thirds majority of states to agree on the proposal presented and it becomes a constitutional amendment. Entirely side stepping the federal government.
This power hasn't been used in a very long time, and from my readings of Washington and Jefferson they intended us to use it. Perhaps this is a corollary to Chesterton's Fence, call it Chesterton's Button rephrased less elegantly than he or you put it: "If your forefathers were willing to die to give you the ability to do something, you should question if that ability has not used in a very long time."
The required majority to approve the output of the convention is 3/4 of the states, not the same 2/3 as to call the convention in the first place.
> Entirely side stepping the federal government.
The entity that is required to call the convention once 2/3 of the states have requested it is the federal Congress, so they are not entirely side stepped. But, it is true that they are not allowed to refuse to call the convention in this situation. There is nothing in the Constitution, any federal statute, or any court ruling that addresses what happens if Congress doess not do so.
> This power hasn't been used in a very long time
It's never been used successfully, although it's been attempted at least once by every state except Hawaii. (Some attempts were indirectly successful in achieving their goal, by spurring Congress to propose the desired amendments.)
https://en.wikipedia.org/wiki/G._K._Chesterton#Chesterton's_...
If your forefathers were willing to die for something, better fully understand why before you try to get rid of it.