I believe there's a sweet spot between reducing interceptions and being too conservative. It's not as easy as just concluding less interceptions is always good no matter what you give up to get there.

Interceptions give the ball to the other team no different than a punt, but with different average field position. Killing several drives isn't worth saving one interception. I don't know exactly how many killed drives the stats say are worth one interception, but I suspect it's less than many think.