Part of the "misinformation" is how institutions are hiding the truth... so isn't censorship reinforcing people's distrust, therefore contributing to the deaths?

This isn't hyperbole, every time some censoring like this happens, it gets factored in as proof of many of the plethora of conspiracy theories. Are these big platforms and government really interesting in saving people, or playing politics? Because it's pretty obvious the main problem is lack of trust, and censorship makes that worse.