ctrl-U used to provide this vital feature and then some eejit decided that that in a browser that should open a window with the page source in it. That was _such_ a painful decision and still enrages me on a daily basis on machines where I haven't persuaded the system to change the keybinding. (where did it come from?).
Ctrl-U can still be made to work (as 'clear line/box'), but it gets harder to find the rune every year. A button to prod for the same function would indeed be a useful alternative.
Like many here I find middle-button paste to be one of the finest things about GNU/Linux, and it's extremely tiresome when you get apps that don't do it right. I really hope it does not get sacrificed as part of the GUI re-architecting that it looks like we are headed for.
I use remote-X-over-ssh for graphical apps fairly regularly and it's extremely useful, but accept the argument that we can achieve much the same effect by other means (SPICE/VNC/NX/whatever). I hope that does indeed come to pass.