Two companies in their portfolios are worth $10B+. I am aware their equity portions are still very small, but I would be surprised if they didn't have the money to afford it.
Many of the YC partners are themselves independently wealthy. Regardless, the domain seems like good branding for YC. Removing the "ycombinator.com" from the address would lessen the connection for new users.
Exactly - the branding is to ycombinator, not just news to hackers.
Having money doesn't necessarily mean you frivolously spend money.