Depending on where you live. The state of Minnesota has a law directly written by labor activists called Earned Sick and Safe Time, which gives 6 days of sick time to every employee in the state. Mental health is a valid reason to use it.
If you're only taking mental health days when you're burnt out, then you're not going to actually help yourself with a single mental health day. There are other signs you need to look for that only you know about. My other signs include a nonspecific dread/anxiety about work without reason, extreme exhaustion, or extreme anger before my shift. Mental health is an "all the time" thing, and shouldn't be gate kept like what you're doing.
Yes, ofc. I agree with all you said. I only pointed out that "don't want to" is not the same thing as any of the stuff you mentioned . I don't want to do lots of things, doesn't mean I can use mental health as a cop-out.
I've struggled with depression and anxiety all my life, and people misusing "Depression" or "Mental health" or "anxiety" for everyday-stuff is undermining the real struggles people have.