The precise terms of the deal between the NFL and the broadcasters are not publicly disclosed so it is impossible to know how payments to the NFL are structured and what obligations the NFL is under as to the halftime show. The economics of the things are indisputable though: the larger and better the TV audience the more the NFL can insist on getting paid. This gives the NFL a potent reason to put on a halftime show with the largest audience and the best possible advertising demographics.
Actually up until this year when the NFL gave up their tax exempt status their books were opened and we knew quite a bit of the details of the agreements. And since no new contracts have been signed since then we actually DO know how payments to the NFL are structured and what obligation the NFL is under at the halftime show. And actually quite a bit of this was discussed in the aftermath of the wardrobe malfunction. Simple put, the NFL does not participate in the halftime show. It’s for the network and the stadium to work out, the network does most of the design and sign up, the stadium tells them whether or not that could actually work. The artists don’t get paid, and they also don’t pay (there was some talk by the league last year about making the artists pay, but that sunk fast).
The halftime show can’t actually generate enough money for the NFL to actually care. That’s part of why last year’s talk about making the artists pay died. The NFL pulls in 5 BILLION dollars a year on the TV contracts alone, and part of how they pull that off is the prize of the SB. It’s a big revenue and self promotion opportunity for the networks, it’s pretty much the only way they turn a profit on their NFL contracts. So the league leaves it alone, and lets the networks use it for themselves. That’s a big part of why CBS had The Who (providers of the theme songs for 4 CBS shows) a few years ago, it was a massive act of self promotion.