I vaguely remember that at one point the NYT provided a way to just simply cancel your account through a link on the NYT account portal -- no need to chat with a specialist. Though, it could have been another paper subscription that allowed for that, I don't remember fully, it was probably 4 years ago at this point.

Anyway, I cancelled my NYT subscription a few months ago and received no push back from the specialist. While this tactic might be something that's expected from management, I don't think everyone is willing to do it... or maybe the specialist I chatted with met their retainment quotas for the month (if that's a thing.).