So could the University of California at Santa Barbara, and it did. You saw where that one went...
Or maybe not. It disappeared into well deserved obscurity within days.
I must assume that a Convention of the States would approach its work with serious intent and limited purpose, as franchised. I doubt it would want to be remembered as a bunch of utopians drunk on moonbeams.
Once a Convention is in progress, I expect Congress will again try to pre-empt the Convention by enacting some more amendments on whatever issues the Convention seems most likely to address. Congress is deathly afraid a Convention would impose really strict Congressional term limits.
IMO term limits are way overrated. They need to be rather loose, but universal in application to prevent people from burrowing into the federal government. One way to do that is a simple sixteen year limit on service in ANY federal elective or appointive position. The feds do have comparative rank positions covering multiple agencies and even the military used for various purposse, so it's easy to limit the appointment position time limit to the equivalent of flag-rank military officers, and exempt the military.