The fundamental limit was discovered by the British physicist Paul Dirac. He knew that in a normal atom, an electron is prevented from spiralling into the nucleus by Heisenberg's uncertainty principle. Electrons are attracted by the positive charge on the nucleus, but any electron trying to orbit too close to the nucleus would be stuck in a very confined space. According to the uncertainty principle that means it would have to move very fast, too fast to be trapped there by the electrical attraction of the nucleus. But if the nucleus has a very large charge, the increased pull would be enough to overwhelm the uncertainty principle.
All electrons spiral down to nuclear oblivion.
So any charged black holes that formed in the big bang could not have collected more than 137 electrons. Any surplus would have been swallowed by the hole almost instantly, cancelling out part of its positive electrical charge. But that's not the only constraint. Any hole that started out with a charge as high as 137 would be less charged by now, because it turns out that electrons don't have to spiral in to be gobbled up. This means that a small part of the existence is always within the black hole's horizon, which translates into a small probability that the electron will be swallowed.