I can agree ability to leave comments could be a switch option but removing comments globally would be a back step.
Regarding those client issues;
you know a client has a contact button?
Also, you could use that same functionality (the comment section) for making the point your all in for satisfying that client “relentlessly”, so that no mistake can be made about that.
Your client may have felt like getting shut up in this case?
Not judging here I don't know anything about your case but theirs always nuances from both sides.
Anyways, a conversation can stay there in the comment section for people hoe would maybe encounter that same problem, they would know about it upfront and also know about a solution to that specific issue mentioned in that conversation.
Also the people that read it get notion about how swiftly you take care of the situation, that can turns a negative into a positive.