Independent retirement would be impossible with 1% returns. With the market's historic rate of return (around 6% after inflation), an investment doubles every ~12 years. A dollar saved at 30 years old is worth ~8 dollars by 65. In a scenario where 1% returns were the norm, a dollar invested at 30 would only be worth $1.40 at 65!

Also, since you wouldn't get much income from investments while retired, you'd have to save way more in that scenario to be able to retire. Sounds like a miserable alternative.