The first rule of medicine is to do no harm. To harm millions of people and kill thousands to save people from a illness (even if you say that these measures help) is a very big mistake.
Lockdown is going to cause secondary social, health and economic problems, but if you can do it well and get control of the virus then you gain flexibility to deal with the secondary problems. If you don't control the virus, you will end up with those other problems as well as the out of control virus.
This is a no win situation. If you aren't lucky enough to live in an isolated country and avoid the problem from the start, something that only worked for some of the really isolated island nations, then you have to move hard and fast to control the virus and hope to deal with the flow on problems once you have the immediate threat under control.
I see a lot of arguments that are along the lines of the only negative outcome of COVID is death, and anything short of that doesn't deserve to be considered. I read your argument as being structured in a similar way.
There are really bad things happening both with the mental health impact of this whole thing, as well as the impact of the virus itself. They're both tragic, and serious, and we need to be thinking about both.
I'm not saying that you're not on-board with this argument, and I'm not saying you are. I just wanted to add this to the discussion for discussion's sake.