In any case, no matter how much they want to squeeze money out of new users, the NYT has more incentive to not have a super strict blacklist, or overly onerous sign-up process. Signup numbers are still metrics that a company vice president/middle manager can brag about, and NYT's initiative of mandating free registration seems much too new (e.g. as a comparison, they had totally free access for more then a decade, then a leaky paywall for several additional years) for them to already have hard enforcement policies in place.
If it's not a blacklist, I think it'd be even stranger for it to be a whitelist, precisely for the reasons you mentioned. mzkply's comment makes me think that it might have to do with Fastmail's email aliases, which is the closest thing they have that's like Mailinator (an email provider that is frequently blacklisted for signups), but I don't think it's similar enough that this makes sense.
I agree with everything you said about NYT's incentives, but that leaves the question raised by this experience.
I opened up a chat with NYT to ask about it, but I was left waiting for an agent there for an hour before I decided to just close the chat.