I think you would be opening Pandora's box.
Let me give the legal answer, and I'll yield to Hostage on the political answer.
If two-thirds of the states request a Convention for Proposing Amendments to "discuss the repeal of the 16th and 17th Amendments," that is the legal scope of the convention, both by the principle of agency and by the 1992 law. A convention could write an amendment to execute a total repeal, a partial repeal -- or it could come to no agreement and adjourn without writing any amendment at all. That's it. If the convention were to attempt to go out of the bounds of the language within the state petitions, it would be illegal and unconstitutional. This is why the 1992 law requires the Supreme Court to be in session during a convention -- to take questions and cases directly without any delay to the process.
I see much more truthfulness and consistency among conservatives than liberals. In fact I see the opposite with liberals.
Because conservatives are powerful in red states which comprise many more states in number than liberal states, I am not at all concerned that the Constitution will be damaged or subverted by calling a Convention.
The agency agreement between states and a Convention wold not allow for amendments that have no broad support to be PROPOSED. A Convention can only PROPOSE amendments, NOT PASS them. Even in the impossible event that an outrageous amendment proposal was produced, it would be impossible still to have it ratified by 38 states or their state conventions.
So it really boils down to which philosophy does one subscribe to, conservative or liberal? If one subscribes to conservatism, they will have no problem supporting the calling of a Constitutional Convention. If one subscribes to liberalism, a Constitutional Convention would be a horror because of the shear number of red states.
And given the country is piping mad right now especially at liberals who have outed themselves to reveal what they really are, an alliance of conservatives with Tea Party independents could with reasonable probability turn more than 40 states red in the years ahead.