The NyTimes is not doing that for "casual use" they are doing it to allow Google's crawler access to the site so it can be indexed and show up on search engine result pages. This is why the incognito trick works on so many news websites.
> that you need to keep killing your cookies
I don't kill my cookies, I just cmd+shift+n to open incognito.
As for supporting sites I value, I visit so many of these sites, and read them, that I would potentially face financial ruin if I had to pay for them all. I get it, I want to support them, but I cannot, not at those prices, not when I can just open my incognito window, and not when even though I pay for the site I still have to deal with ads that roll down content as I'm trying to read it.
And I imagine you might have adblock enabled while you're sitting there judging me about not giving them cash for accessing the site. ;)
Re: Incognito Mode - the reason that works is it starts you out without any cookies. You've effectively cleared "all" your coookies.
Re: Supporting these sites - if you would really potentially face financial ruin, then that's a much different reason than you originally gave, which was that you felt like you would be a jackass for reading a site that you could hack into for free. The "I can't afford it" at least makes sense. I've personally decided that $3.75/week is worth it for me , but your financial situation may be different than mine, and I can at least appreciate that logic.
Re: Adblock - don't use it - though, not for any desire to support the sites, just isn't a big enough deal for me to worry about it.
Have you considered that if you are reading the site so often that you need to keep killing your cookies, that you perhaps might be getting some value from the site, and it wouldn't be unreasonable for you to to reward the creators of such great content?