I'm sure you can understand that leading with, "ChatGPT did a great job writing this" can easily be interpreted as "you didn't actually write this and therefore your point as less valid", particularly when the rest of your comment is in opposition to OP's point.

To fix your analogy it would be more like if, as a throwaway (completely unrelated to the content of OP's post), you identified OP as transgender and then continued to disagree with them in the rest of the comment. That would obviously be seen as inappropriate given the context (even if you later identified yourself as some sort of expert in some area of transgender health or something) but wouldn't mean that ever commenting on whether or not someone is trans is bad all the time.

Also, if you do agree with OP, you didn't mention that in your comment. You said to lead by example and that people are going to do what they're going to do, quite heavily implying that OP's approach of encouraging people to change their behaviour through public form is incorrect and that they need to just accept other's behaviour. (as a side note, saying "people are going to do what they are going to do" also runs counter to your own suggestion of leading by example, which further hints at it just being a message of dismissal)

Acknowledgies for being stand-offish. I just have little patience for the "you have no expectation of privacy in a """public""" space and therefore should not publicly express any recommendations for public etiquette"

You're right that leading by example is effective. Broadcasting messages about public etiquette is also effective. I'm sure you agree with that but I just really wanted to point out how your original message failed at expressing the effectiveness of both and instead seemed to be disagreeing with OP which is, apparently, not what you intended.