If the page is lazy loading content then the local ctrl+f is not going to work, obviously.
If you’re hinting at an argument about whether lazy loading content should exist, that’s a separate discussion. In my experience, pages that override ctrl+f do it for a good reason
I think I've seen one page override ctrl-f for good reason -- it was a page that lazy loaded literally millions of lines of text that wouldn't have fit into RAM.
Every single other page that does it just wastes my time. It's always a super janky slow implementation that somehow additionally fails to actually search through all the text on the page.
Even in those cases I'd prefer to just be able to natively search the content that has been lazy loaded. I've run into more than one website where the search functionality they bound to control-f is horrible.
If you’re hinting at an argument about whether lazy loading content should exist, that’s a separate discussion. In my experience, pages that override ctrl+f do it for a good reason