LEDs do emit incoherent light, which makes it difficult to observe interference patterns. However, it is not difficult to make two sources that are coherent and have a stable phase relationship with each other...an antenna makes it easy, a bit more difficult would be lasers locked to a common reference, or one laser split along two paths. In fact, a laser shining through two slits or pinholes is equivalent to this, and shows the interference pattern you'd get.
The real answer is that even if you have coherent light sources with opposed phases, the fact that the sources do not originate from the same position will keep them from canceling out at all points. You get interference patterns, just not patterns such that "no light energy reaches most observer positions". With more sources, you can confine the emitted energy to smaller, more sharply defined areas or spread it out, but you can't make it go away, the best you can do is absorb it. And there is no way to emit both from the same location...this is simply equivalent to not emitting anything.