The accredited investor standard doesn't prevent you from losing money.
It prevents people from marketing investment products to you.
Even if you're unaccredited, you can still invest in private company stock: it's just legally risky for the company that sells it to you, since the law makes it very easy for you to sue them.
The reason the accredited investor standard has teeth for startups is that if you're taking money from unaccredited investors, you're almost always taking it in small amounts from lots of people. The law assumes --- reasonably! --- that if you're doing that, you're marketing your stock as an investment product. That makes you, in effect, a public company, and you have to follow all the same rules as other public companies do.
I too have always been a bit miffed about the whole accredited investor thing, but that angle had never crossed my mind.