A kid drops out of high school, plays video games instead. Two years have passed, now he has a two year career gap. "Eh, I'll just stay home and figure something out." Now he has a four year career gap...
If you have a survival stipend, it's probably a lot more common for qualified, competent people to have career gaps. I probably would, personally. That makes it easier for the depressed kid to compete whenever he decides to rejoin the job market. (Also, for some reason, parents who set up trust funds tend not to worry about this....)
Also chances are if the depressed kid stays home for a few years, he will find some calling he actually likes - programming, music, writing, some specific type of research, whatever - and come out of it with a particular qualification to do something. What's the benefit to the depressed kid of having him flip burgers and stack shelves and have no time to figure out what he actually enjoys?
Treatment for mental health problems is expensive. The underlying issues can have causes that require a lot of time to solve. Therapist trips are expensive. Some of it isn't covered by your insurance. You lose a lot on productivity as a parent of the kid. You will need to dedicate time to him unlike in other situations where you can be fine delegating the responsibilities.
A kid drops out of high school, gets depressed instead. Two years have passed, he can't afford the treatment and needs to get out but his issues aren't resolved. He is forced to work, burning himself out. He can't be productive or do critical creative work that pays well. Now he has gone 4 years without being treated, having time to recover and is in a worse position.