The idea of accredited investors horrifies me. The only way to get rich by investing is to get in early when the valuation is very low. These type of rules guarantee that only people already rich will be able to get in early. The reason cryptocurrencies & ICOs are popular is they let anyone speculate and day trade.
That said, contrast the S&L crisis [3] with Bernie Madoff's fraud [4]. The former lost $160 billion of regular Joes' money (along with wealthy investors'). $132 billion of taxpayer money had to be spent, alongside countless hours of regulators', judges' and lawmakers' time, again, on the public dime. A minor political crisis started (and subsided).
With the latter, $70 billion was lost (though it might have been as "small" as $20 billion). Prosecutors and judges still got involved, but fines repaid their efforts. Systemic effects were largely contained.
TL; DR We restrict the masses from illiquid investments procured through irregular channels because (1) the legal costs of diligence preclude small investments, meaning small investors either invest at a material disadvantage or invest too much (relative to their worth) and (2) the lower your worth, the higher the probability that a busted investment will lose you your shirt. That turns a financial problem into a de-stabilising political problem.
Side note: early-stage investing isn't as profitable, on a risk-adjusted basis, as it might seem if one only counts the winners.
[1] https://www.sec.gov/fast-answers/answers-accredhtm.html
[2] http://www.finra.org/industry/qualification-exams
[3] https://en.wikipedia.org/wiki/Savings_and_loan_crisis
[4] https://en.wikipedia.org/wiki/Bernard_Madoff#Size_of_loss_to...
Disclaimer: I am not a lawyer. This is not legal, nor any other kind, of advice. Consult an investment adviser and a securities lawyer before making risky investments.