I've heard it claimed that broadcast nets do take a loss, or barely profit, and the benefit to them is it lets them promote their other shows so it's a bit of a cascade effect. But I don't think anyone knows if that's actually true.The current model only makes sense if networks take a loss, which is only feasible for a short while if it's your loss leader or something (E.G., NBC / EPL ).
The economics for broadcast nets and cable are different, and both are trending down. ESPN's woes are well known, mostly due to people cutting cords. They and other cable companies make most of their revenue from subscriber fees. They pay for sports to justify giant subscriber fees which are charged to everyone regardless of whether we watch or not. Which has led to the cord cutting that is starting to kill them.
Meanwhile the broadcast nets have been losing viewers on everything including sports but making up for it by raising rates. They could do this seemingly impossible thing -- charge higher rates for fewer viewers -- because they still have the largest single chunks of eyeballs and advertisers have no alternative if they ever want to reach a substantial audience. But they are starting to face push back on that as well.