Private ownership of the means of production is more orthogonal to workers rights. There are capitalist economics in countries with very strong workers rights and unions, but where the means of production are still privately owned. Capitalism is fully compatible with strong family and medical leave protections, even though those who own the means of production are disincentived in the short term from giving workers rights. The fact that the US is worse on workers rights isn't a problem unique to capitalism.
The first allows no-reason, no-notice termination of employment by both parties (which doesn’t really work - the employee usually needs income more than the employer needs a single employer).
The second is related to the ability to unionize.
That's true but it's also exactly what you go to court for. Then the court audits and determines if this was a coincidence or malice.
That's why employers don't often make it this obvious. Like firing an employee 3 days after announcing they are a protected employee.