It won't show up in too many real photographs with artistic intent (challenge?)
Are you kidding? It entirely depends on the type of photography I suppose, and no doubt that an f64 proponent will care less. :-)
The previously posted image was for illustrative purposes only, but the issue is that any background blur is drawn by the aperture shape. If the shape contains angles then the resulting background blur may draw multiple edges when blurring a contrast edge. (Like ni-sen, perhaps partially related to it). Also, the slightest hint of a singular contrast point will result in a vague reproduction of the aperture shape. If the aperture shape is not perfectly round, then it will be distracting, simply because of the way our eyes and brain operate.
As for artistic purposes, it makes an interesting challenge indeed. I don't think it is a very uncommon situation compositionally. A sharp foreground subject with heavy blur in the background. (Especially in macro shots?). Here is a particular case were I was actually trying to add it specifically to the image for "narrative" purposes. Following is the most useful series that I got from 2 days of trials:
The challenge is primarily in two elements:
1. The blur circles, which need a very specific contrast to become subdued white-ish circles and are very illusive to capture, and thus are hard to "place" in a relatively predetermined position.
2. The foreground depth of focus, which should preferably create enough sharpness for the entire group of flower buts. But that can only be achieved in two ways, either moving further away from the subject, or stopping down. I hope you understand the dilemma there.
To get the blur circles flat white-ish takes a particular kind of filtered contrast. I can reasonably predict the bokeh-rings from the viewfinder image but I suspect that that is very camera specific. I'm still undecided where to place the flower buts exactly and how much blur I will allow. Even so, great learning experience.