If you choose to stand on the legal pillar that says a COS cannot make dramatic changes, then yes, the current constitution is not legal because the delegates that went in 1787 did not have the power to draft a new constitution.
That said, I am of the opinion that anything can come out of a convention which is based upon our known history.
To that end, I do not wish to see any kind of convention where delegates gather believing they are supported by the power of the people.
The Declaration of Independence did not meet with universal approval in the colonies. And I'm certain the British parliament did not consider it to be a legal document. There is always risk in politics.
The prospect of a packed SCOTUS etc. leaves me to believe a COS might eventually be the only way to avoid violent upheaval. That is the basis of my opinion.