If they've not been educated about not doing that, there's a fair chance they aren't going to be too smart around other big security issues either - such as resetting passwords with very little validation of whether it's the genuine customer requesting it or not.
Unless the customer is causing you a major amount of aggravation or costing you money, you shouldn't be happy to see one go.
Also, FWIW, I don't think citing a comment in which the commenter calls the OP an "egotistical bitch" twice is good support for an argument.
As for cherry picking that quote from the comments, that is fair. I did not read his sexist diatribe, i just read his opening statement and concurred.
"Wow, you are a hell customer. In the future, set a temporary password. They were trying to help you and you have to be a mouthy egotistical bitch. I'm sure they're happy to see you go. As someone in customer support, I'm sure they're happy to see you go. Egotistical hipster bitch."
For not wanting to give her password to customer support she is somehow a "mouthy egotistical bitch", a "hell customer", etc.
And yet you get down voted for mentioning the misogynist word?
You can agree that she might be wrong but I think the sentiment is that some of the people that are disagreeing with her are being specifically sexist in their method of disagreement.
A hell customer would call them up, yell, demand answers, and refuse to hang up until the situation was "fixed" to her liking, threaten to sue and call CNN, etc.
Most support agents are probably ok with seeing a staunchly unsatisfied customer simply leave and allow them to help people who want to be helped.
"Wow, you are a hell customer."
I'm willing to bet Squarespace is happy the OP is leaving their service, I know I would be if I were in their shoes.
Granted, it is a case of bad support, but as Colin mentions, it is likely an issue with an under trained new hire, not a systematic failure.