I've been building a hermitage with hexagon-shaped farm plots, and I love this idea... the ability to build walls and fences at irregular angles would be fantastic. As mentioned, there could be a minimum angle of 45º to prevent the weirdness that might arise from having a cornerpost with eight walls sprouting out from it in all directions.
We're already able to rotate and fine-place other structures to a very high degree of accuracy (using ctrl-shift and mousewheel), so I'd see this as more of an extension of that system. Place and build a cornerpost (maybe even make it so you can rotate the cornerpost on placement as well?), right-click it, extend, and then get the option to more finely control the angle of the extended wall by holding ctrl.
You can already create irregular fencing with trellises, which can be more finely manipulated in the manner described above.

Unfortunately, you can't extend them automatically like fencing, which makes it a bit more tricky to see where they'll terminate.
The main challenge for players would be getting the final extended wall to align with the first cornerpost so you can seal it. It would require a lot of planning. But, of course, those who don't want to bother would still have the option of building walls at right angles.
I think it would make settlements look much more organic, rather than everyone's village looking like an army base.