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It's not about requirements so much as aesthetics. Pots are chosen for their proportion and coloration, finish, feet, etc. Cascade pots generally are deeper for the balance they provide, although pots as tall as they are wide are more in favor now than the very tall ones.

As to shallow pots, while we don't always use the smallest pot available, that is the direction we go. Depending on the size of the tree and the thickness of the trunk (not to mention the horticultural needs of the tree!), we choose what we believe is an appropriate pot.

Here is a link that might be useful: Bonsai Sashi-no-Eda

The shallow pots are not only to restrain growth of mature bonsai that have been ''finished' in terms of styling (though continue to grow and need maintenance trimming), but because they are simply showcasing the trees, presenting them as if on a tray, rather than being the heavier e.g. terra cotta 'flowerpot' supporting different types of 'full size' plants. The cascading trees are in taller and wider pots to balance the weight of the cascading branches as much as for esthetic reasons.

Excuse me, lucy, but didn't you just say exactly the same thing bonsaikc did? Why don' you add something new?

Lucy intoned that the initial assertions of the OP where part of the story, that looks like something new FWIS.

I might add this:

Bonsai, like most art forms, has its root in a natural phenomena; when trees find themselves growing in areas where the roots can't go deep (as in growing on solid rock) the tree itself can't grow tall. It becomes naturally dwarfed and this is what the first bonsai artists (who were Chinese, not Japanese) collected and worked with. Since the rootball was relatively flat, a deep pot was not necessary. Whether they knew it or not, the shallow pot places emphasis on the tree and not the pot--what a revelation! The rest, as they say, is history...