the prologue glasses are only once per roster (it says so in extremely tiny characters under the glasses’s icon when you click “skip prologue”). You can pass them between your characters but you can use them only on classes of the same type (e.g.: berserker and gunlancer)
you don’t really miss anything, doing it once is enough.
the only possible reason you might want to do it on another character is if you don’t feel you want to punch Kharmine’s face in with enough fury