In the current behavior, when you press ctrl + f and start typing, you append your search term to your previous search term. My proposal is to make pressing ctrl + f select the entire previous search term, such that when you start typing, you would overwrite it. If you do wish to append to your previous term (which is way less common in my experience), you can still press the right arrow key to deselect the text and append text as you wish. For me, this would solve quite a bit of frustration when forgetting to type ctrl + a after ctrl + f, as this is the only application I know that does not automatically select the previous search term.