I think the people who think a new constitution would be something they 100% agree with.
The constitution has a process for amending it and has been numerous times. The Constitution also provides for a way to legislate to adapt to changing times.
Let's take the Second Amendment since it has a lot of controversy. If you cannot get it amended then how do you expect to get an entire new constitution approved?
Also from a practical matter how would a completely new constitution be adopted? A majority of a popular vote?
Here is a read that might be of interest. https://www.cbpp.org/research/states-likely-could-not-control-constitutional-convention-on-balanced-budget-amendment-or