If they're also afforded the same responsibility, sure. Because if people had the same rights as banks, I'd be free to gallavant down to Vegas, blow all my money on slots, and expect the government to vacate my debts and pay for my steakhouse dinner
And how would people get services typically offered by a bank? Sorry but most of people on this planet need banks because they don't have enough cash to buy real estate. Are you suggesting that people should not own their homes?