Isn't this what the "gig" economy is leading us to? Uber is very similar: you aren't an employee, so no Social Security, no workman's comp, none of the hard-fought labor gains of the 20th century.
If you have good alternate options (eg another startup trying to hire you etc), you can demand better conditions.
I assume you're referring to stocks of the company in question (or possibly its competitors as well). For a private company, you can't trade stocks outside company-approved periods anyway, so would this really be an additional restriction in practice?
You can get access to the books as a shareholder specifically 'For the purpose of valuing my shares", but then if you decide to buy or sell shares based on what you learned (and what other use is there to valuing your shares?), you're insider trading?
It's selling restricted stock that's the big problem. You can do it, but it's complicated, and there are waiting periods.
[1] https://www.sec.gov/news/speech/speecharchive/1998/spch221.h...