Yes, the states propose the convention, but if you read the clause closely it says that Congress calls the convention. Therefore, what do you do if Congress refuses to call the convention if the states ask for it? What if the Congress delays a convention indefinitely or unreasonably to manipulate election outcomes in the state legislatures?
On another note, we really ought to amend Article V to make the amending process clearer. There are a lot of very gray areas in the Article V amendment process which ought to be be amended to clarify things like how long each state has to complete the ratification of an amendment, whether a state can withdraw its ratification once they've given it as long as the amendment isn't ratified yet, whether a state can change its vote from no to yes. What happens when the US uses the military to compel states to ratify (like in the Civil War which also rigged the state legislatures with the rump legislatures)? Who gets to determine when the ratification has been properly done? What if states are added in the middle of a ratification process, do you use 3/4 of states at the time it was proposed or 3/4 the number of states at the end of the process? etc. All of these are real questions that have come up at some point of US history. The amendment sounds so straight forward when you read Article V, but in reality there are some serious problems. It could use a little clarification.
This is what is known as the elusive Constitutional Crisis. If we look closely at the pertinent excerpt, it says... "...on the Application of the Legislatures of two thirds of the several States, shall call a Convention..." emphasis added
I believe the operative word here is "shall". For 230+ years, the Republic has survived because when push really came to shove, we had people that did the right thing. This is always the question - "What happens when, when it matters most, people don't do the right thing". I don't know.