Of course there is a down side.
The State feels its power slipping away, an Article V convention would be used as a method to try to re-centralize the power.
If we have said convention, there will be no First, Second, or Fifth amendment. The State has been trying to dissolve those for decades (though old political theory says that free speech, armed citizens, and the State not being able to lock up whomever they want is a bad thing).
Those Conventions would be hijacked as soon as they are called, if the movement is not being manipulated right now.
I suspect my legislature is typical of the other 56, minus CA, IL, NY(?). It is a part time gig, in session for three months. Most reps are independent business people and know very well of the heavy DC hand. My rep is a nurseryman, 1,000 acres under cultivation and 150 employees. He doesn't need the added time burden required to be a rep.
I'm saying we shouldn't equate state pubbies and democrats with their pompous, tyrannical cousins in DC.
Article V is the only peaceful means we have. Let's use it.
The left does not need an Article V convention to succeed in the mischief you describe, they are doing it every day and you and I are powerless to stop them apart from an Article V convention.