It takes both. Analytics can give you a macro view and identify patterns, but one big problem in football is quantifying things. Two things anyone around here has heard me talk about is the misunderstood impact of pass/run ratios and time of possession. Why do they get talked about so much? They're in the box score. Neither is in there necessarily because of importance, just intrinsically. Many things you'd want to know, like drive based stats, aren't quantified easily. Most stats involve the ball, most of the game doesn't.
Another important distinction is analytics are best at telling us something happened, but generally poor at telling us why. That's where the tape is invaluable. I would encourage anyone that isn't using analytics to use them, very valuable, but know their limitations. They're a supplement to traditional scouting, not a replacement.
I agree with everything you are saying, and I said as much in my post, its a tool nothing else. Billy Bean took a team to the World Series using analytics and now it is all gospel. It is a tool use it, but trust your eyes as well.