A bit like audio compression - if everything is compressed to the same volume then it gets really hard to tell how loud things are relative to each other.
Another problem is people encounter stories where there are anecdotes in the other direction e.g. today I read stories about Ticino, Japan, Germany where hospitals are waiting for an influx, but it doesn't seem to be growing in the expected way. Why? Unclear. These stories of course get less attention.
The problem with your way of arguing is that one can not win. If they say "if we don't do anything there will be 3 in 100 people dying" and they do something, you say they lied. If they don't do anything, you will ask "why have they not done anything! They are incompetent or malicious"
Clickbait-style "everyone in New York is dead!" bad-faith hysteria would erode my trust.
"We saw a terrible situation, and communicated the situation as clearly as we could at the time, even though our information was incomplete. Since then we have more facts, and are striving to communicate them to you" enhances my trust, not erodes it.