It may or may not be useful, depending upon the circumstances.
In some cases it can be useful as a visualization technique. The representation is low-dimensional, and often 2-dimensional -- which means it can be visualized. That said, there are many other methods of representing data in a low-dimensional space so it can be visualized, and it's not clear that self-organizing maps are the best way to do that.
Sometimes self-organizing maps are used as a general form of clustering, and can be useful anywhere that (unsupervised) clustering is useful.
That said, I agree with your general reaction. Often, self-organizing maps aren't very useful. I would not expect neural networks or other algorithms to benefit from being combined with self-organizing maps. Self-organizing maps don't really solve any clearly defined problem, and probably aren't of all that much use in many/most practical situations.
If you had never heard of self-organizing maps, you probably wouldn't be missing much (in my personal opinion).