I would agree with you except....
When players get scholarships, it's based off stats... when players get letters and accolades in college, it's based off stats.... when those players get drafted, their draft positioning is based off of stats....
(If that's not true, name me one quarterback or any other player drafted in the 5th round who had better stats than someone drafted in the 1st round and I'm not talking about a player who's draft status dropped due to injury. I'll wait....)
When players make it to the NFL and their rookie contract expires, they are paid according to their stats.... players contracts, bonuses, and incentives are paid according to their stats..... when a player, his agent, and the general manager are all in the room negotiating a new contract, what arguments/proof/measurements are they using??? STATS!!! Players are selected to the pro bowl, largely due to their stats.... (some of that is popularity too)
Lastly, when a player is inducted into the Pro Football Hall of Fame, they get in according TO THEIR STATS!!!! They don't get inducted because of their wealth, skin color, looks, businesses, who their wives or girlfriends are, or the weather pattern.... they're inducted because of their STATS!!!
To end it there.... the great Bill Parcells said, "You are what your record says you are". Last time I checked, that's a stat too, so that matters.
I think Parcells has a lil more credibility than BB, because Parcells made teams good wherever he coached. BB only looked good because of Tom Brady. Parcells never had to ride the the coattails of one player. He literally created Hall of Famers in different cities.