You are right! because the states must ratify the amendment and that is a very high bar indeed.
However that does NOT change with a convention of states. The convention is only for PROPOSING amendments. The amendments themselves still have to be ratified by the states so there is no more chance of amending the Constitution to eliminate the 2nd amendment with a COS then there is if congress proposes the amendment.
In other words, we have nothing more to worry about with the 2nd amendment using a COS than we do if the dems control congress and that holds true of any proposed amendment. The COS is only for proposing amendments. Our congress is not going to propose a balanced budget amendment so we will never get one unless the states convene a COS and first propose the amendment. Once proposed then there is a chance the states will ratify the amendment and congress will have to work within a balanced budget.