The problem with that reasonning is that it applies to pretty much every "risk", without consideration of quality. What you're saying is "better safe than sorry".
I'm sure you wouldn't suggest putting everybody systematically in quarantine for a flu epidemic, every year, makes a lot of sense. Yet the death rates for influenza is much higher than coronavirus atm..
Overplaying increases the baseline of perceived risk, so you'll have to overplay it even more next time to provoke the same reaction. That's difficult, because once you're at "we're all going to die with 99.9% certainty", will people really care tomorrow when it's 99.99% or 99.999% the day after that?
It feels a bit like throwing antibiotics at everything. Sure, it's effective in the moment, but you're lowering the future effectiveness.
I'm sure you wouldn't suggest putting everybody systematically in quarantine for a flu epidemic, every year, makes a lot of sense. Yet the death rates for influenza is much higher than coronavirus atm..
edit: much lower -> much higher