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In some sense they do. Ionic chemicals are just things that are attracted together and can pack together to make a solid. They aren't "bonded" like covalent chemicals, they are just attracted. We write NaCl, but really every sodium is just attracted to the six nearest chloride ions. The same principle applies to a statically charged balloon.

But with static electricity the charges involved are much smaller and the particles are bigger. In salt you have single atoms with missing (or extra) electrons. In static electricity the particles are huge (10^17 or so atoms of it's dust) and the charge is much smaller: like hundreds or millions of elections meaning the charge to mass ratio is 10^10 less. (these numbers are of the top of my head, but the principle is correct)

So lower charge + higher mass = weaker bond.

They also aren't consistently sized, so you can't get the consistent packing of particles like in a salt.

>For the instances where individual molecules are charged, why do they never form ionic bonds as a result of being charged?

They actually do in many cases. For example, a molecule like acetic acid can lose a H+ ion to become acetate, which has a negative charge, and it can form ionic bonds with sodium to form sodium acetate crystals. In these crystals, negatively charged oxygen atoms from the acetate ion are ionically bonded to the positively charged sodium ions. Different crystal structures can form depending on how much water is present.

Isolated pairs of ions don't tend to stay associated in this manner for a variety of reasons (at least in the condensed phase such as an aqueous solution), but as long as they can form a regular lattice with the right energetics, molecules are perfectly capable of forming ionic bonds.

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A cat with a balloon stuck to its fur is just a really really big salt.