The NFL is getting pretty convoluted with their overtime rules, specifically playoff overtime and the "not being able to kick a FG on the first possession and instantly win" stuff. You're right that it is a bad idea. But you're wrong to think it's a fair comparison to the shootout fiasco. In short, they still play football in the NFL to settle football games, and a shootout simply ain't soccer.
Here's a hint: bring up the NCAA overtime rule - I can't defend that nonsense at all.