I should probably clarify this a bit.
It's true that HN sponsors Launch HNs (and Show HNs) by YC startups. This is in the FAQ: https://news.ycombinator.com/newsfaq.html. However, YC would not be funding HN if that were the only reason for it. It's a secondary factor.
Far more important than promoting existing startups is attracting founders who might start new startups. This requires an entirely different strategy than promotion: it requires being interesting enough to attract the right kind of users. That's why the site is organized around curiosity, as I explained elsewhere in the current thread (https://news.ycombinator.com/item?id=46309399).
For more on this, here are past explanations:
optimizing for curiosity - https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sor...
relationship between HN and YC's business interests - https://hn.algolia.com/?dateRange=all&page=0&prefix=false&so...