Stigma is a huge problem, especially when initially seeking help. Burnout took years to be added to diagnostic manuals, and still people are scoffing whenever someone drops out after being worked to the bone for months.
In Finland, burnout is not considered a valid reason for sick leave. Depression is, so people are only given sick leave if they accept that diagnosis and medication.
It's basically the same in the US. Taking care of your "Mental Health" is corporate speak for burnout. There is talk about avoiding burnout, but if someone has to actually take leave because of it, there are no legal protections for burnout, but there are for mental health issues. Mental health can be treated, but burnout is harder to come back from in the eyes of the company.