“They can put restrictions on how their delegates act that the president is unlikely to”
Not so. Whether called by POTUS or the ghost of Eugene McCarthy, it’s still a 100% State affair. Rest assured that every state will bind their delegates to things they believe important.
And no matter what comes out of the convention, 3/4th’s of all states legislatures must vote to approve before it becomes an Amendment.
Yes the states can put restrictions on their delegates. The states that have already passed article V resolutions have put specifications on their delegates. Not all are the same