A not unreasonable one though: a large part of why minority shareholdings have actual potential value is because of a dense network of regulation that ensures company executives act in shareholders' interests, respect their property rights and make accurate representations about how the company is performing. So shareholders have an interest in the state enforcing securities law, including how shares may or may not be marketed.

On the other hand, provided wishing wells and ICOs don't claim to be a genuine investment and aren't considered to be equivalent to securities by anyone with any common sense, it's arguably state overreach to stop people chucking their money into them.

Basically, its illegal to market exotic investment opportunities to unaccredited investors (for good reason IMO). Same reason only accredited investors can invest in things like CDOs and weather derivatives.

Could you do an ICO or BTC share sale to only accredited investors with an online form asking for details a statement to that effect?

I recall from angel funding that the criteria is that you must ask, and that you must have "no reasonable reason to doubt" that a person is an accredited investor. The language is nice and vague, as per SEC regulatory standards.

Yes, exactly that. Compare it to designer drugs, where some reasonably well-understood chemical compound is made illegal, with the effect of creating a market for a similar chemical that is worse understood and may be more dangerous (i.e. less beneficial) to the consumer.

https://en.wikipedia.org/wiki/Designer_drug