So why would anyone oppose this?
I rather imagine that most people would be opposed to a Constitutional convention because there would be no practical way to control the agenda of the convention. The result would be attempts to make wholesale changes to the existing Constitution and current Amendments (2nd, 10th, etc.) to suit the leftist, socialist agenda for the future.
Oppose this particular notion of laws applying equally to the Congress as the people? Nope. Oppose a CC to get it passed? Yep.
We can vote them out as the election cycles roll around, if we have the stomach for the fight. It won’t be any easier with a Constitutional convention.