Not all keyboard-only users are blind. In light of this, one of the main things to focus on in keyboard accessibility is that you can tell when something has keyboard focus.
I've noticed at least three places where SE fails this.
First, in the answer sorting tabs - active, votes, and newest. If I tab to any of these buttons, there's no indication that the focus is there - I have to look at the bottom of the page to see that it's pointing to a link, and then based on the end of the URL see what button currently has focus to be able to change the sorting.
Another place is when you open the image uploader. You can open the uploader with CtrlG, and the focus automatically will go to "browse" (so when you press enter you'll be able to find your image and upload it), but you can't visually tell that that's where the focus is.
And the third example is deleting your own comment. I can tab to the delete button, but the button remains invisible and you can't see that the focus is there at all.
There are probably more examples, but these are the three that I noticed.
If you're confused as to why it's important that things be accessible without the mouse, please read up on keyboard accessibility. While I thankfully don't have any physical problems with using a mouse, I'm using my time with a broken mouse to give accessibility feedback so that people who need it can get a better site experience.
<label>for a hidden input and doesn't itself receive focus. In the first case, tabs should be getting a light grey focus highlight but maybe it's not strong enough.