One of your key premises, that investing in startups is a key / good path to getting rich, is flawed. Investing in startups is notoriously NOT that stable of an investment vehicle. If you're a small-scale enough investor to not meet accreditation rules, why would you WANT to throw 10k at a startup?

You speak in terms of rights and that's one debate to have. But evaluating the material harm in this situation, the notion that this denies upward economic mobility in a significant way seems overstated.