Russell Brand 
When is it appropriate to ask for references?
Employers do it all the time.
And Landlords.
Very occasionally customers.
Why not employees?
If it were common to ask, it might be a source of suckagereduction. And any company suggesting it as fair game might gain an advantage in hiring, presuming the obvious issues of anonymity of the existing employees was protected.
Let me propose a thought experiment:
If you were one of those three references, what would you say about your company? Would you encourage some to work there or to steer clear?
What would say are the best things and the worst?
Can you replicate and expand the good things? Perhaps at least write a blog post about them?
Can you help remediate the bad things? Or at least tell someone about them?
Should you be working there or perhaps you too should be part of the “great resignation.”
