You've mistakenly assumed that there are "proper" rules for bonsai pots. There are those pots that look good with bonsai and those that don't--regardless of shape really. The shapes you've mentioned happen to be the most effective way to subtly enhance the tree without being ostentatious or distracting. They are the "go to" shapes that can make a tree or trees look good.
Unnusually shaped pots tend to upstage the tree. That's not what a good bonsai pot is supposed to do. Pots are supposed to underscore or accent the tree or composition, not the other way around.
Ovals, rectangles and variations of those shapes help contain an image most effectively, while lending a supporting visual image to the tree. Pots that veer away from those shapes, like dodecahedrons, quadrangles, pentagons, pots with animal feet and other stuff
, can work, but are MUCH harder to incorporate into a pleasing design. Usually they simply look weird, silly or are downright ugly.
The pots Nick Lenz works with are made with individual trees in mind and that's why those pots "work." He knows how to meld idosyncrasies of unnusual trees with unnusual pots. It's not an easy thing to do. His pots emphasize what the tree has. The trees were not chosen to suit the pot. The pot was made to suit the tree.