This misses the point. Websites are allowed to replace default keyboard shortcuts for a reason. There are only a few exceptions to this, like Ctrl+W. In other words, you can design your website however you want, except to make it more difficult to leave. This is an implementation of the same philosophy.

> you can design your website however you want, except to make it more difficult to leave.

Who decreed that page navigation is in scope and search navigation is outside?