I think, like most men, I'm more visual than statistical when it comes to knowing what's good and what isn't so good. I know from that list of QBs in the OP, the ones I've seen play regularly and multiple times, who and who isn't a Hall of Fame QB.
Granted, I'm biased as a Steelers fan, but other than the success of Tom Brady in New England, there's not been a more consistent, more talented, more determined and bigger gamer than Ben Roethlisberger in the QB position in the last decade and a bit he's played. A little less so now, but through his early years Big Ben was almost impossible to take down and he made something from nothing multiple times every game. Roethlisberger has also played behind what has been almost consistently a fairly weak offensive line that has given him little protection. He's played his entire career in what has been, until this year, the toughest division in football and much of the time, by the end of the season, he's got multiple injuries that would take down most QBs and he still gets out there if at all possible. Even in his last game, three weeks ago, he had a torn meniscus and came back on the field trying to will his team to a win when it was clear he just wasn't effective. And now, after surgery following that Miami game, he's back on the field practicing and the suggestion is he's going to play this weekend if cleared to play with pain.
There are very few teams in the NFL who wouldn't love to have Ben Roethlisberger as their starting QB and there are very few teams, if any, who wouldn't be better with him as their starting QB. That's easy for the eye to see just by watching the games, without any stats to get in the way. Sports is far more than nerds and their statistics and the truly great players are easily identifiable just by watching them play.
Roethlisberger will be a first ballot Hall of Fame inductee and I'll be shocked if anyone with a vote doesn't vote for him.