Again, not every team is built equally or playing from the same deck of cards.
It works for Atlanta, fantastic. It's not Rizzo's job to worry about how Atlanta constructs its bullpen, it's Rizzo's job to construct the best bullpen possible for the Nats. Rizzo doesn't care if he is paying one RP double what the entire Atlanta bullpen makes, nor should he. It's his job to improve his bullpen, and Venters & Kimbrel aren't walking in that door. So he spent some money.
Why spend money on relievers? You shouldn't if you are working with a TB budget. In that case, it's the last thing you should invest your limited funds on.
But if you have the money to do it, a better question is why not? I would say the Yankees certainly got quite the return on their $11M investment in a setup man last season. It's the Yankees, they have that luxury, and it paid off. Sure, the Yankees or Nats can go the Tampa route, but why? They don't have to roll the dice like that and hope some bum turns it around the cheap.
It's not like Washington gave Soriano this deal at the expense of filling a different hole. This is a late signing that was done after the rest of the team is already set.
You can make a good argument that they would have been better off signing one of the cheaper closers earlier in free agency, or taking a chance on Brian Wilson, because none of those options would have cost them a pick. $14M rotting away in the bank isn't going to put this team over the top, but Soriano might. Again, this isn't a battle of who can be the most efficient, it's a battle of constructing the best roster possible. If Soriano is even close to what he's been six of the last seven seasons, it's a good move. If he flops, the biggest mishap here is the lost pick, not the money.