Easy, the people have no control once the convention is approved. They have no requirement to listen to the states, the people, or follow the rules the convention was created under. They can, with a simple majority, make their own rules. They are likely to go well beyond their mandate, and there are serious questions about how the delegates would be chosen, and how many each state would get. How would you like it if it was population based and then used to radically change the constitution based on a simple majority vote of delegates? CA, NY, IL get to set the agenda and we get no say.
Whatever they come up with and vote for becomes an amendment, there is no backstop of states getting a vote on it once the convention is approved. It is far too dangerous, and makes no sense to risk the things we have for unknown future stuff that we are unlikely to get anyway from a convention.
States Likely Could Not Control Constitutional Convention on Balanced Budget Amendment or Other Issues