Electrons require significant voltage to move through free space or insulators. They generally move between places by hopping between atoms with free outer electrons. Electrolytes are designed to not have any.
That sounds better. Still leads to some questions that I am missing the answers to:
A Lithium ion has the same charge in magnitude as an elecron. Electron is much lighter. Why and how is it that Li+ ions are able to, but electrons can't?
A same number of ions and electrons should be generating on the electrodes.
>> Generally move
When there no free electron space in atoms, instead of electrons being stuck, should still move the electrolyte as free particles just like ions.