That focus style isn’t just there for keyboard users you know? What about the case where a website has loaded and launches a modal dialogue (not uncommon and a pretty standard practice). You’ve moved the focus to the lightbox, the user closes the lightbox by pressing [escape] (again, all normal, standard interactions). Now what is focused, and how does *any* user know that this is the focused element of the page?
Basically what you’ve done is remove the wheelchair ramp for aesthetic reasons, and put it back somewhere that is hard to find and isn’t accessible to everyone who needs it.