Can anyone explain why having polymer connected in 2d sheets is better than connecting in all 3 dimensions?
Maybe a self-assembled 3D lattice would have some disorder due to the extra degree of freedom which translates to structural weakness.
However, single crystals are inconvenient as materials, because growing a crystal (i.e. self-assembling it) is a slow process.
Moreover, growing a single crystal so that it will have some useful form is difficult for a few forms and impossible for most forms.
Therefore the normal way to make something from a single crystal is by growing a large crystal and then removing much of it, leaving only the desired form.
Because of this disadvantages, making anything out of a self-assembled 3D lattice, a.k.a. crystal, is restricted to a few applications where the properties of a single crystal are essential, i.e. various electronic or optical devices.
In most cases, the most convenient materials are either thermoplastic materials, i.e. metals, glasses or thermoplastic polymers, or materials that are produced in a soft plastic state and after forming they can be transformed into a hard state by some treatment, i.e. ceramics, cements or thermosetting polymers.
A disordered 3D lattice is an amorphous material, e.g. a glass (unlike a crystal, which is obtained by very slow cooling, to allow time for the self-assembling of the ordered lattice, a glass is obtained by very fast cooling, which does not allow time for ordered self-assembling) or a thermosetting polymer.