It's unclear to me if we are disagreeing on anything or merely stating the same things slightly differently.
> The tragedy of the commons applies when there's a non-zero marginal cost. But with zero marginal cost, you have have to find some way to cover your expenses, and then you can give away the rest as a public good
So a web page isn't zero marginal cost, it's nearly-zero. Servers require occasional maintenance and continuously consume electricity (to say nothing of the rent / peering arrangement that is usually part of gaining access to someone else's network). Even though a server can host a million individual pages at near-zero marginal cost for each, the original point still stands that if nobody is paying for that server and nobody finds "some way to cover your expenses," the electricity will stop flowing or it will break down and nobody will repair it. So everyone hosting on that server is doing so at the mercy and pleasure of the org or individual paying for the server's continued existence (i.e. a patronage arrangement). Your specific examples (NYT giving some content away and public broadcasting giving all of it away) are examples of patronage models in action (NYT non-subscribers are patrons of NYT, and public broadcasting itself is a patron of its sponsor base).
> [citation needed]
I believe you gave a fair explanation of why Coke doesn't consider an ad vended to a broke person to have zero value immediately after that request for citation, so I will cite your logic. In addition to your observations, the points about brand stickiness (that "when someone offers you a soda, they want you to ask for Coke" bit) and behavior shaping still apply (source: I worked in advertising, this is common knowledge in the industry, but if you want concrete sources I can hit the Google and try to dig up a primer on the industry philosophy; it's so bedrock-knowledge that I can't remember precisely where I learned it). But you're right; even absent those effects, Coke assumes that people who are broke right this moment aren't broke tomorrow and still want you thinking about buying their beverage. "Coke doesn't consider an ad vended to a broke person to have zero value."