What I use is Home/End with selection {Ext+(Y,S+L)}, after which you can delete {Ext+O} or cut or copy the line as fits you.
There's also some more advanced movement/selection tricks as detailed in the BigBag Extend topic, but I don't use those much.

I know that's not a single key command and you may want one, so if you need it a lot you could add it as an Ext-tap command or on one of the Extend layer keys you don't need. To get a kill line with EPKL for Windows, you'd use something like this:

α{Home}+{End}{Del}

Or maybe select line is best after all? It's certainly a bit safer. If you want that, remove the final {Del}.

Excellent point! I suppose that's more like what BPH wanted and Emacs/Vim do. In the code above, for a proper line kill with the line break use:

<l>     = α{Home}+{Down}{Del} 	; l -> Delete/kill current line (remove {Del} for line select)

(Shown here as a Dead Key, I tried it on {tap-Ext,l}.)