Pretty annoying that it’s illegal for me to invest in any of these newish tech companies.
It's not illegal for you to invest in Stripe. It's simply illegal for Stripe to try and sell you their stock. If you happen to have personal connections to Stripe leadership, and they haven't hit the regulatory shareholder limit (after which they must start filing disclosures with the SEC), you could legally buy all the Stripe stock you could afford.
Have you seen an example of a regular middle-class person actually doing this? Because in all the stories I've heard, company leadership just say "no, you need to be an accredited investor to do that", and that's it.