If you think this is actually about such concerns, I congratulate you on your having been able to maintain a child's naivete for all these years.
I'm not saying the league is acting out of benevolent concern for the safety of its fans or anything, but yes, I do think that preventing any sort of terror-inducing event at an NFL game -- or at least having publicly taken precautions -- is a major motivator for this rule.
There is money at stake here that dwarfs the sales lost from people sneaking alcohol into stadiums, or using their own seat cushions, etc. Even the mighty NFL needs to buy event liability insurance for every game, and the insurers use every public disaster as an occasion to force clients to tighten their security or face premium hikes. There are also constantly changing legal regulations for event security at city and state levels, many of which are also tightened ad hoc to events like the Marathon bombing.
And this isn't even taking into account the blow the NFL would take if something ever DID happen at a game. First, the PR hit would be deadly, and second, there is the very real danger of decreased family attendance. Clearly, the owners are already pricing out the kinds of fans who sneak alcohol into stadiums in favor suburban families and status-seeking yuppies who spend money recreationally, and this tactic is way more effective than a ban bag would be.
Searching bags more thoroughly would either require spending money on added security personell, or exacerbate the problem of long waits and cramped, chaotic lines at stadium entrances -- and faster lines means getting more people inside earlier, with nothing better to do than buy stuff.
Compared to these concerns, the fraction of a percent of fans sneaking booze into games don't even show up on the radar. And as for seat cushions, I'm willing to bet that a lot of stadiums will make them available either for free, like the 3D glasses at movie theaters, or for $1 on the honor system, like the bins of headphones at most airport gates.