TAMPA, Fla.—Veteran defenseman Braydon Coburn worried that the Philadelphia Flyers had traded him to a hockey wasteland when he was dealt to the Tampa Bay Lightning in 2015. Coburn had started his NHL career in Atlanta, where the franchise struggled at the box office and fled to icier pastures in Winnipeg. He wondered if Tampa, with its 75-degree weather in the dead of winter, would be a rerun.

But as Coburn drove with his family through various neighborhoods looking for a house to rent, he couldn’t believe what he saw: hockey...