"male and females of dioecious shrubs could be braided to make sure that the resulting tree produces berries"

This wouldn't be needed since Ilex verticillata can be pollinated even when they are tens of feet apart. And I can't see this improving the appearance of these loose, informal shrubs since it would tend to crowd the berried stems.

Personally, I don't see the appeal of this at all other than creating some sort of garden oddity. But then I much prefer to allow plants to grow as nature intended, pruning only to improve growing conditions. But if you do want to attempt such an experiment, any young sapling shrub with a single flexible stem will work. Caning or multi-stemmed shrubs would just complicate the process IMO. This is done with azaleas, Rose of Sharon, wisteria and ficus trees, as well as other houseplants but it is a long term process, much like creating a bonsai specimen or training a shrub into a standard or tree form.

Shaping trees.

I
have been inspired by those 'oddities' that I did read about. This 'braiding'
thread is equivalent to 'grafting' threads about 5-different-apples-in-1-tree,
tomato-potato plant, etc. Why not?

The fruit trees and vegetable grafts are done to improve fruiting or condense the number of different plant needed. Grafting is a dead common practice in all realms of gardening, however braiding is not and accomplishes nothing to further fruit or flower production (or increase disease resistance or facilitate clonal reproduction) so not equivalent at all. It remains just an oddity or conversation piece.

"oddity or conversation piece"

Well, you decide whether you want this in your garden or not. Chances are if a grower puts it on the market, then there are buyers for it.

It looks like a high maintenance contrivance more apt to be found in Alice's Wonderland than in a typical garden,...even a gardener's garden. Three plants planted separately would produce a similar effect with a lot less work. It is pretty though, but not for me.

That said, I tried braiding a few plants years ago. One of the braids would die or end up being a lot smaller than the other two. After a while I said the heck with it. Too much trouble and I had other things to do.

I
would think that nearly all money tree owners bought a braided plant, they didn't
braid the plant themselves, it would be the same here. There won't be much
difference as to plant care either. Not sure if 3 (or 5 in case of the money tree) separate plants have
the same visual impact, I would say that at least the braided trunk has an
additional visual impact in a stand-alone specimen planting. Let's hope growers pick up on the biz opportunity :-)

It isn't that complicated after you get the skill down. The photoshopped rose of sharon above can actually be plaited because they (and most hibiscus) have flexible stems.

http://forums2.gardenweb.com/discussions/4136184/forsythia-to-plait-or-not-to-plait?n=14

I will take some pictures. I thought I did, but couldn't find them.