That's a natural assumption, but if you think a step further it's not hard to see why it's false: you shouldn't optimize for local optima, especially if doing that would ruin your global optimum. When you have a goose that lays golden eggs, don't risk the goose for an egg.

YC's economic interest in HN is having it be a happy, thriving community. That dominates all other considerations put together. A fast way to ruin that would be to destroy the community's good faith by suppressing negative posts about YC or YC startups. In addition to being wrong (we wouldn't want to belong to such a community ourselves), it would be dumb. If anyone wants more explanation there are posts about HN vis-à-vis YC's business interests going back years: https://hn.algolia.com/?dateRange=all&page=0&prefix=false&qu.... See also https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que..., which describes the simple way we try to optimize this (simple in principle, though not in execution). And see https://blog.ycombinator.com/two-hn-announcements/ from 2015 about HN's editorial independence.

(Edit—because I've been wanting to write about this for some time and this may as well be the place:)

The above is the answer I always give to questions of how HN serves YC's business, because it's true and it's solid economics. It's the right answer to give to anyone who's looking at the question through a cynical economic lens (as we all have been trained to do) since it basically says "we can be even more cynically self-interested by not doing that".

However, I also always feel a little bad after giving that answer because it's not the deeper truth. The deeper truth is that we just feel this way. HN and YC grew up together. In a way they are siblings, and one doesn't exploit one's sibling. Or, to switch metaphors: because HN and YC grew together, the connections between them are complex and organic, like the connections between brain hemispheres. If you get in there and start snipping and moving things around, you'll probably lobotomize yourself.

If you want a hard-nosed business reason for how HN makes money for YC, one is: it leads to people starting startups that wouldn't otherwise exist, and it leads to YC funding startups that it wouldn't otherwise get to fund. That's how HN adds to YC's core business (edit: but see [1] below). I use that reasoning to explain to people why we don't need to sell ads on HN or do other things to monetize it or drive growth. Again, though, it doesn't capture how I (and I think most at YC) really think and feel about HN. The deeper truth is the two have always been together and we can't imagine them otherwise.

In other words, the value of HN to YC is intangible. That affects how we operate HN. If the value were tangible, then snipping things and moving them around and generally being bustling and managerial would be the way to go, or at least the most likely thing that people inside a business would do. But since it's intangible, all that kind of thing gets supplanted by a general feeling of "this is good, don't fuck it up". Since the main indicator of whether we're fucking it up or not is the community, the way HN can most add value to YC is by keeping the community happy. Happiness means interest (HN is supposed to be interesting) and trust (a community can't exist without trust).

This is not a paradise that will last forever—it's a historical accident that an internet forum ended up in a sweet spot vis-à-vis the company that owns it, where the business is better off optimizing for the forum being good and happy than by banner ads or growth hacking. But we all know that it's an honor to get to be stewards of a community in that way, and while nothing lasts forever, we want to keep it going as long as possible, and maybe longer than one could reasonably have thought possible.

[1] edit: for some reason I forgot to mention the three formal things that HN also gives to YC: job ads for YC startups, Launch HNs for YC startups, and displaying YC founder usernames in orange to other YC founders. See https://news.ycombinator.com/item?id=23293437 for more.