Yes, but there is a component of experience that matters here, it is the ability to handle yourself and your personal problems professionally. Someone on the job for 10 years, even if they were suffering from mental illness, if they demonstrate the ability to deal and handle it responsibly (monitor it and take preventative or restorative care, including following doctor's instructions about "fitness to work"), it is important, because they can prove themselves reliable and trustworthy colleagues, and show emotional maturity and good judgment. However, someone with less than a year's experience, they have not demonstrated that ability and stability, therefore they need to be monitored more closely, both by colleagues and supervisors. This is actually at the heart of the matter of what happened here, this guy (the co-pilot) was not able to handle his mental health issues properly, likely was not receiving proper care and did not follow doctor's instructions regarding being unfit to work and didn't report that to management, as required. My argument here is that such inexperienced/ young pilots need to be monitored more closely, until they are proven more reliable behaviorally/ emotionally/ professionally, including technical knowledge and judgment.

I am not saying that someone may not develop mental health problems later in life or their career, but having a track record of knowing how to cope with your personal issues and managing your wellness and functioning professionally is important, some people never succeed in that in the first place. Having a track record of doing that successfully for several years is generally a good predictor of being able to handle subsequent problems, as the best predictor of future behavior is past behavior. Of course it is not a guarantee, and other systems should also be in place, like enhanced mental health monitoring and support, and probably mandatory reporting of "unfit to fly" by doctors directly to management, for all pilots regardless of experience. As for the Egyptair case I cannot comment, this is a different culture with different standards and preventative measures regarding mental health (suffice to say that they didn't even accept pilot suicide as the crash reason, as mental health is a taboo topic in several nonwestern cultures).