You either vet the security and anyone can invest, or you don’t vet the security and then sell only to people who are more able to be defrauded without becoming a burden to society.

It sure feels like that, but the general spirit of the law is that they don't want fundraisers putting up TV ads to invest in <insert company>, which end just being scams.

This is actually the spirit of accreditation - it's more to do about how you promote securities as opposed to simply filtering out a portion of the population due to net worth.

I think the slightly longer answer is that the SEC emerged as a way to regulate and moderate the cycles of investment capitalism that dominated the US economy for over a century: the bank insolvencies and speculative bankruptcies of the westward expansion; the fraud and corruption of the pre-Civil War and Gilded Age/Long Depression; and the evasion of state regulations and rampant double-dealing by financial institutions in the 1920s — plus the boom in junk finance, lightly-regulated developing world bonds, and boiler room operations as the SEC was deregulated in the ‘80s, to say nothing of the emergence of complex derivatives in the ‘00s. As a result, the operating mental model of regulators is that investments require strong regulatory oversight, because loosening restrictions has uniformly wreaked economic havoc.

However, they also have to balance systemic risk agai st the need for access to the capital markets for smaller (and, yes, riskier) companies, which is why we have reg D offerings. Traditionally, the balancing test has been whether the “accredited investor” can be expected to have access to knowledge and expertise sufficient for them to understand the risk of unregulated and often complex offerings, such as convertible notes. In practice, this usually covers institutions and high-net-worth individuals, who have no excuse for not availing themselves of such expertise, or at least are less likely to lose their shirt if they don’t do so. Systemically, this prevents people from rushing into less-regulated, more risky investments that could create the kind of fiscal and political instability that marked earlier panics — reg D offerings may be riskier, but this way the SEC can manage just how many people are exposed to that risk. (You can, justifiably, be cynical about the fact that very large institutions will happily sink tens of billions into high-risk investments and get bailed out thereafter, but that leads to the question of whether it’s actually worth tightening regulation at the price of reduced financial innovation.)

BTW, the SEC has also recently opened up 501(D) criteria so a lack of net worth can be balanced by an appropriate professional or educational background that would give the investor the ability to judge risk, though I don’t think this has functionally changed the definition yet in the field.