Sculpture is a better analogy to bonsai than a painting. As bonsai is 3 dimensional. Unlike sculpture, or actually similar to some specific sculptures, in bonsai various tricks of perspective are used to create the emotional, or visual impression of a large tree from nature. These tricks of perspective often require the viewer to be in a particular location relative to the bonsai. If you don't use tricks to force a sense of perspective, you don't need to have the viewer in a particular location relative to the tree. One can also build these tricks to force perspective into more than one side of the the tree.
There are quite a few bonsai that have more than one "front". Some really are viewed from all sides. Some really have a distinct "front". It varies widely.
Young trees in training - it is a useful exercise to "pick a front", but don't get too attached to it. Stay flexible in your thinking. There are many "design rules" that are guidelines, rather than hard and fast rules. The guide is that in general the tree as it rises to the apex "bows" toward the viewer. This is a trick to force perspective. Deciduous trees, especially formal brooms and informal brooms have branches reaching up and arching out on all sides of the tree, meaning that any ( or rather several sides) side of the tree will have the effect of forcing perspective. These trees can have many "fronts" or can be viewed "in the round".
Single trunk tree styles, particularly the triangular "idealized conifer" styles very often require the viewer to be only "in front" of the tree.
With a young tree a useful exercise is to pick a front based on a particular trait. Mark it on the outside of the pot, then pick a different front based on a different trait. Some of the traits you can (or should use are below) When done with the exercise you will have 5 or more marks around the pot, but likely a few will be grouped more or less together. The region with the most marks is probably your "best front"
-Nebari - the spread of the roots
-Width of the trunk a couple inches above the soil line
-where the line traced by the trunk is the most attractive
-jin or shari or deadwood feature is most attractive
-branch structure & placement is most attractive
-other special feature of the tree is most attractive
If any one feature is particularly attractive, it can drive your choice of a front. If no one side of the tree has multiple attractive features, you either have a boring tree, or one that is very well suited to being viewed from all sides.
For young trees, I prefer round training pots in order to be easily able to view the tree from all sides.