This is the absolute worst thing that could happen. Today's political problems do not stem from the Constitution. They stem from the fact that our government, along with most others, is now effectively privately owned and controlled by financial elites who control by terror. The governments we see are maintained as mere theatrics (along with all other forms of mass entertainment) to maintain social order.
Politicians at both the state and federal levels are for the most part just paid actors. The purging of dissidents, widespread MKULTRA operations, and other covert war crimes now taking place under their watch are bad enough. It is unacceptable to hold a Constitutional Convention while lawless criminals hostile to liberty wield the reigns of power.
The Constitution may be a flawed document. Many segments of society have never been properly protected as they should have been. However, the Bill of Rights (the first ten amendments to the Constitution) flows directly from the Declaration of Independence, a statement of divinely inspired principles.
As the Declaration states, the rights expressed therein are "unalienable" and derive from the Creator; they exist independently of any government or system of law. Actions of government inconsistent with those principles are illegimitate on their face. Any attempt to touch one hair of the Bill of Rights should properly be viewed as an overt act of war against the people of the USA.
The agitation for a constitutional convention is being sponsored by a group going under the name of "Citizens for Self-Governance." The reader will note that an outline of a five pointed star is created at the top of their logo. The left and right angles of the star are partially obstructed by the "thumb" of each hand. This is a stylized version of the "eye in the pyramid" motif.
This is a state-sponsored covert operation designed to manufacture popular consent for a constitutional convention.
That all being said, it seems apparent that a new American Civil War is being deliberately fomented and designed from the get-go to fail. See Is the Patriot Movement Controlled Opposition? for further information.