The NFL's US TV deals, when put together, are for 7 billion a year. The ads themselves are not all managed at the highest level: There are national ads, regional ads, local ads... A big part of what a TV network does is manage the ads themselves.
While a large majority of the fans have broadband, they don't necessarily have something connected to the TV that will output the NFL streaming apps to their living room. There's also no proof that advertisers would pay the same rates for ads than they do for over the air TV.
Handing out the rights to TV stations also has all kinds of other advantages. You don't have to pay the TV stations to advertise the games. There is all kinds of content in said stations that could also be considered advertising: A team will be covered more in the channel that also carries the games than in one that does not. If you have an NFL app as the way to show the games, now you are the one paying the TV stations so that they cover your stuff. The NFL might get a bigger share of the pie, but other people are a whole lot less interested in helping the NFL grow its fan base. And yeah, the moment you start offering all games online bypassing live broadcasts, without at least a modicum of an attempt of blacking out regular TV broadcasts, the networks will balk at you, so if a pro sports league wants to move to online, they have to either only show content that the local TV stations do not want, or go all in, because the TV networks are not going to be happy competing with the league directly with the same content.
Good luck keeping an attempted switch secret too: To move broadcasts inhouse, a league would either have to purchase new equipment and crews, from the engineers at the stadium to the commentators, or to downright poach them, neither of which is easy to do.
So even if it's theoretically possible they'd make more money online, the risks and the political costs of doing such things are tough. We've seen how a player strike harms a sport's financials. A failed move online would be just as big, if not worse, and completely self inflicted.
While a large majority of the fans have broadband, they don't necessarily have something connected to the TV that will output the NFL streaming apps to their living room. There's also no proof that advertisers would pay the same rates for ads than they do for over the air TV.
Handing out the rights to TV stations also has all kinds of other advantages. You don't have to pay the TV stations to advertise the games. There is all kinds of content in said stations that could also be considered advertising: A team will be covered more in the channel that also carries the games than in one that does not. If you have an NFL app as the way to show the games, now you are the one paying the TV stations so that they cover your stuff. The NFL might get a bigger share of the pie, but other people are a whole lot less interested in helping the NFL grow its fan base. And yeah, the moment you start offering all games online bypassing live broadcasts, without at least a modicum of an attempt of blacking out regular TV broadcasts, the networks will balk at you, so if a pro sports league wants to move to online, they have to either only show content that the local TV stations do not want, or go all in, because the TV networks are not going to be happy competing with the league directly with the same content.
Good luck keeping an attempted switch secret too: To move broadcasts inhouse, a league would either have to purchase new equipment and crews, from the engineers at the stadium to the commentators, or to downright poach them, neither of which is easy to do.
So even if it's theoretically possible they'd make more money online, the risks and the political costs of doing such things are tough. We've seen how a player strike harms a sport's financials. A failed move online would be just as big, if not worse, and completely self inflicted.