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.
See my post # 25.
If the amendment would take the first option (see below) there would be not constitutional convention to
deal with. Plus this would also put the pressure on
the house & senate members to vote on this amendment in public.
The first method is for a bill to pass both houses of the legislature, by a two-thirds majority in each. Once the bill has passed both houses, it goes on to the states. This is the route taken by all current amendments. Because of some long outstanding amendments, such as the 27th, Congress will normally put a time limit (typically seven years) for the bill to be approved as an amendment (for example, see the 21st and 22nd).