[charonn0]

By longstanding convention. Ctrl-F is the conventional in-page search combo, while a dedicated search field is the conventional website search engine.

[croes]

But it's about inpage search, it's just a lazy loading page.

The dedicated search field is for searching my websites and the result would be a list of my pages that contain the search term. Ctrl-F jumps to the location of the search term on the page I'm already at.

[folmar]

You can even use the OpenSearch description and move the search field to the browsers'.