This is actually does work to some degree, but appears to be buggy in its implementation. The problem with Extend is that you have to pick the curves near the end to extend or it doesn’t work. The main bug is it is possible to re-select the selected boundary curve as curve to be extended, which is wrong and needs to be fixed.
You can crossing window (right-left) select the curves to extend, as long as you get somewhere past the halfway point on the side to extend it works - but if you hit the boundary curve (or a curve already extended?) it fails.
A trick here is to use Lasso with crossing selection… Lasso does work as a polyline fence if you do not hold the mouse button down but just click points as if you were making a polyline. But it doesn’t seem to get everything unless its closed, so I just dragged it as usual.
See quick video for success and failure modes.
Oh, and I wonder if a separate ExtendCrvsToBoundary command would be useful, where one could preselect curves to extend and then the boundary, and the ends of the selected curves nearest the boundary would get extended to the boundary.