Mental health checks sound like a good idea, but there is a risk that it prevents people from actually seeking help.
See the way mental illness is treated in aviation - mental health care is inaccessible to pilots because seeking help for serious issues will put a black mark on your record and end your career. So pilots with serious mental health issues intentionally avoid getting help.
Not that it's a bad idea just that it's not as easy as it seems. Penalties for seeking medical care push people away from seeking care and in turn make the health issues worse.