MIAMI—Public-health officials say statewide lockdowns implemented early and aggressively are necessary to curb the coronavirus pandemic. Florida Gov. Ron DeSantis disagrees.

Among the states in the U.S. with the most coronavirus cases, Florida alone has refrained from imposing a statewide stay-at-home order. The Republican governor has instead focused restrictions on the hardest-hit counties while seeking to spare other areas from the deep economic pain that comes with a lockdown.

“There’s...