Publicly traded stocks comply with SEC regulations, which have a lot of provisions about properly informing the public, reporting on material events, etc. There's no ban on the general public making private equity investments either, if the company is willing to register the offering with the SEC and comply with similar requirements.
What's at issue here is just an exemption from those requirements. If you have relatively few investors and they are all deemed to be sophisticated investors, Congress has decided that you can waive the usual investor-protection rules, cut out the SEC's involvement, and negotiate your own conditions directly with the investors. The rationale is that if you have relatively few and presumed-to-be-professional investors, those investors know how to negotiate appropriate conditions on their own, rather than relying on SEC protection, so are allowed to do so. Sophisticated investors often have a "term sheet" they offer (vetted by their lawyer), or else have a lawyer on retainer to negotiate terms with you individually. If you're offering an investment to the general public, on the other hand, the assumption is that they probably don't have a term sheet handy or a lawyer on retainer, or really any knowledge about this whole sector at all. So in that case you need to comply with the regular disclosure and investor-protection rules. But you aren't banned from taking on non-accredited investors, as long as you're willing to comply with standard SEC terms.
The practical problem is that registering your offering with the SEC and complying with the disclosure requirements has pretty high fixed costs, so is often considered prohibitive for small companies. Therefore there's kind of a rule of thumb that you should avoid non-accredited investors in order to fit in the exemption, at least until you grow bigger, which is where I think the myth that you literally can't take non-accredited investors originates. (My own preferred solution to that would be to streamline the system to reduce cost of compliance for small companies, rather than expanding the definition of what constitutes a sophisticated investor.)
Yes. A lottery ticket is one dollar, and people know that the chances of winning are infinitesimally small.
The difference is that a cold-call from a a convincing enough salesman can get someone to invest too much money in what is essentially a different type of lottery in the best of circumstances. In the worst of circumstances you have: pump and dumps, Ponzi schemes, etc.
Publicly traded stocks are subject to a large number of regulations that have the intent to protect investors. The point isn't to make it impossible to lose all your money; the law will gladly let you give it all away if you so choose. But the idea is that people should have the necessary information to know what they are getting into. In exchange for exemption from SEC registration requirements (which are costly for a small company to deal with) and less disclosure, companies can only deal with accredited investors.
Publicly traded companies are required to regularly make disclosures to their investors and the SEC. Not that most people read these disclosures ... but in theory, there's less of an information asymmetry than with private companies.
The lottery is usually a state-owned monopoly, so in theory, society as a whole back the cost of gambling. Or the state is simply unwilling to give up its own cash cow.
