physical chemistry - Why do aqueous solutions always have to be electrically neutral?

I was reviewing some analytical chemistry and stumbled upon a section that explained the imperfection of using a salt bridge.

It said that the using dissimilar ions is a problem because in, for example, the case of KCl the K+ and Cl- have different mobility and so you get regions that are rich in K+ and others rich in Cl-. This means that some specific parts of solution (even though it's small) to be not electrically neutral i.e. electrically charged.

So I imagine in theory at least it must be possible to somehow extract these charge-rich areas and put them into a beaker. So what is all this I've been learning about solutions having to be electrically neutral?

Answer

Because the electrostatic force is much stronger than you can imagine. Yes, you can get charge-rich areas in a cell. However, the amount of charge held here will be negligible. A rather small amount of charge can overcome the field near the plates and prevent more charge from approaching. The amount is quite small; it's not something that you would notice (and it won't give you a static shock¹

^{1. Everyday static shocks are stronger by orders of magnitude because they deal with a lot of charge accumulated on the surface of an insulator, while here it is a relatively small amount of charge dispersed through the volume of a conductor}