The purpose of accreditation in these types of off-the-book investing is so that only people who can suffer deep losses can bet on them. The government is at least nominally there to ensure that more traditional investments are conducted fairly and legally. Things like angel investing, e.g., are sort of wild west in their approach, so rather than ban them, the government has taken the position that only those with really high risk tolerance should be able to participate. In practice, this rule is rarely enforced (due to the off-the-books nature), as far as I'm aware (only dimly).
I think one could easily construct an argument against accreditation, since it locks out average people from early stage investing, which is where lots of money can be made. But if I'm not mistaken, the SEC's position is that it's far more often where money is lost. Institutions and professional investors are far more likely to be able to make a distinction between a snake oil salesman and a legit business opportunity. The SEC gives a pass to startups who don't have the resources to make official equities sales, with the caveat that they try not to take advantage of people who aren't sophisticated.