An activist investor’s suggestion this week that Walt Disney spin off ESPN rekindled a long-running debate over what the company should do with a sports network that has been a major profit engine for years but whose subscriber base is eroding.

Daniel Loeb’s Third Point LLC, which owns a small stake in the entertainment giant, told management in a letter Monday that there is a “strong case to be made” for Disney to part with ESPN, which would result in a company that is “no longer haunted by the specter of cord-cutting,” or consumers canceling their pay-TV subscription in favor of streaming services.