It costs nothing to produce one more unit of a digital good (or add one more customer to a digital service). Prices in economics are affected by supply, and supply is limited by the marginal cost of production. If there's no marginal cost, then there's no limits on supply, and price tends to zero.
Startup economics agrees with this. If the cost of acquiring a customer via paid advertising is $9.99 and the lifetime value of a customer is $10, then the smart thing to do is to spend every single dollar you can raise on paid advertising (I exaggerate slightly). The value we place on the actual production of that service for each new customer is zero.
This completely messes up traditional economic models.
Having sold digital goods for years, I can attest that this is not true. For example, customers have questions, which consumes one's time. They do returns. Fraud costs. Accounting costs. Taxes on transactions. Bandwidth costs. Hosting costs. Transaction fees from your merchant service account. Etc.
I guess it would be more accurate to refer to the cost of producing one more month of service rather than one more customer. Even then there are costs, but they're tiny compared to the costs of providing a physical service.
Contrast the costs of running Netflix now vs Netflix when it was distributing DVD's in the post (or the costs that Blockbuster had). Adding one more customer to Netflix costs so little now that it's effectively zero, compared to the direct costs of sending out DVD's in the old days.
Ever notice that online companies hide from their customers? As in, no phone number, no email address, no way to contact support, they just direct you to a FAQ. This is because customer service is very expensive to provide.
It could be, it just depends on who owns the web service. Could be a corporation, could be a social-minded B corp, or could be a non-profit.
https://letsencrypt.org/ is run by a non-profit, and would be considered a public service. Consider how much "profit" they're removing from the economy by offering the service for free, and yet one could argue the value of every site able to obtain an SSL cert to receive free TLS support is greater than that profit.
TL;DR Things are complicated. We keep trying to find physical world analogies for the digital space, and that just isn't going to work well.
Clean air and national securty also cost money to maintain, but have no user fees.
It won't happen tomorrow, or a year from now, but it'll happen in our lifetime.
Essentially, humanity is freed from 'work'
Edit: I'll give you am example that might fit the definition: DNS