RALEIGH, N.C.—Working as a lifeguard used to be a hot summer job, but not any more. The gig, glorified in movies of the ’60s and decades since, is now hard to fill, and not just because they won’t let you bring your cellphone to work.

Time was, a buff youngster in Ray-Bans and a red suit could spend the summer cultivating a tan and scoping the scene while being paid for the service of protecting people from drowning. In the era of “Where the Boys Are” and “Beach Blanket Bingo,” you could occupy a power perch above the pool,...