I think some worries/Anxiety can be helpful -

eg if people worry about getting lung cancer, so they quit smoking

or they worry about car accidents, so they avoid drink-driving, avoid driving with bald tyres, use snow chains, don't speed, don't drive tired

or they worry about skin cancer, so they wear a hat/a long sleeved tshirt/sunscreen

or they worry about sexually transmitted diseases, so they use condoms/a dental dam/ask their partners to get tested

I often think a lot of human suffering is caused by people being too blase about risks.

Mind you, some risks are so infinitesimally small that there is no point worrying about them - the last person hit by a meteorite wasn't killed, just badly bruised, and that was Ann Elizabeth Fowler Hodges in November 30, 1954.