The anxiety we are talking about here is exactly the kind of anxiety you _don't_ want. If there was no vaccine in the short/midterm future people would probably (and somewhat rationally) assume that everybody (or rather 60%) will get the disease at some point, which would mean that the reward for behaving cautiously now is a lot worse (at least on an individual level, it would still be necessary not to overwhelm hospitals or to protect certain high-risk-groups).
You might be inducing a "so-what" mentality where people don't want to refrain from going to bars and restaurants just to not catch a virus that's going to get them at some point.
Not enough anxiety, in my opinion. Tons and tons of people are still behaving as if everything is normal, or that they are somehow special.