The reason you can't buy a share of Uber or SpaceX is, effectively, that those companies don't want your money. Both could easily do a public offering and admit you as a shareholder, but choose not to.
Further clarity: I'm "accredited", and I don't think I can buy a share of either company either.
P.S. I think it would be a very good idea to buy some Uber shares before their IPO. Maybe try EquityZen [1].
But sure, maybe Uber and SpaceX aren't the best examples. Not sure if I'd even necessarily invest in either of them myself, but I thought they made for relatable examples. For a more real-world case, I'd love to be able to invest some money with the solar funds run by Wunder Capital, and that seems a lot safer than crypto, but that's off-limits to people like me as well.
Regulations rarely work as advertised; however, their 'unintended' side effects do seem to be quite effective in terms of creating artificial barriers to prevent the working class from moving up.