Eu não acho que há nada no cânon para dizer que o Gringotts não oferece contas comuns também. Mas o uso de cofres é tradicional na sociedade bruxa, então se você tiver um, você o usará.
Note que todas as pessoas que vemos ou ouvimos usando o Gringotes em canon são ricos, descendentes de sangue puro ou ambos. Aqueles que não podem comprar um cofre e não herdaram um, no entanto, podem usar contas simples: nós nunca o vemos pessoalmente.
A cena em Pedra Filosofal , onde somos apresentados ao Gringotts, certamente sugere que as contas comuns estão disponíveis:
About a hundred more goblins were sitting on high stools behind a long counter, scribbling in large ledgers, weighing coins in brass scales, examining precious stones through eyeglasses.
Além disso, de Relíquias da Morte :
"But I thought we were looking for places You-Know-Who's been, places he's done something important?" said Ron, looking baffled. "Was he ever inside the Lestranges' vault?"
"I don't know whether he was ever inside Gringotts," said Harry. "He never had gold there when he was younger, because nobody left him anything. He would have seen the bank from the outside, though, the first time he ever went to Diagon Alley."
Harry's scar throbbed, but he ignored it; he wanted Ron and Hermione to understand about Gringotts before they spoke to Olleander.
"I think he would have envied anyone who had a key to a Gringotts vault. I think he'd have seen it as a real symbol of belonging to the wizarding world. [...]"