QB is indeed the most important player on the team.... but they are still only a small portion of any given win or loss, especially outside the horrific (who don't last long) and the elite. Why would you measure a QB by a result he has far less control over instead of the many ways we have to measure the things they have a high level of control over.
You make some good points, though I disagree that it's a "worthless" stat for QBs. But let's think about that last statement you made. What does a QB have control over, really?
He can control a play they change to at the LOS. Like, a play comes in from the sideline, and he looks over the defense, and he has total control over whether to audible to a different play or run the play as called. Or he can audible for a change in protection. So that's one thing.
He can control - to a large but not unlimited degree - where he throws the ball, both in terms of choice and in terms of accuracy. I say not unlimited because there are elements (wind, rain, snow), there's pressure put on him, and there's always the chance of a tipped pass or someone knocking into his arm as he throws. But largely this is under his control.
That's about it.
He can't control:
- The weather.
- The pressure put on him by the defense unless it's due to him making a mistake in what play/protection he calls.
- The routes run by receivers (whether they run the route correctly or not).
- The quality of job the defense does on the receivers.
- Whether other players commit penalties that nullify good plays he makes.
- Whether receivers drop easy, well thrown passes, or, conversely, make incredible catches off poorly thrown passes.
- Defensive penalties that nullify bad plays by the QB.
- Results of tipped passes - sometimes they fall harmlessly to the ground, sometimes they even get caught by his teammates, and sometimes they get intercepted.
- Yards gained after the reception - though the QB can influence this with a perfectly thrown ball to a receiver catching it in space and in stride, a lot of this work is done by the receiver himself through speed, agility, breaking/missed tackles, etc (it's normally why we attribute YAC to the receiver not the QB).
So based on all that, what statistic(s) measures best the things that the QB does have control over?
Completion percentage? If a QB turns down a great opportunity for a deeper pass in order to dump it off for a safer, higher percentage pass, that might look good in the stats, but it may actually be representative of poor decision making. Conversely, he may take a risk and try for the home run which may be a good gamble, and might be the play that their coaches all love, but it may result in an incomplete pass or worse, and interception. So that would go against his stats, yet would actually be a good play by the QB.
Yards per attempt (and its variations like AY/A, etc.)? Well, sure it helps as a stat but it's also flawed, given all the things above that he can't control. A QB doesn't see a guy open downfield and, fearful of making a mistake, dumps it off to the RB in the flat for what should be a 2 yard gain on 3rd and 8, but the RB breaks three tackles and goes 73 yards for a TD. Yay, great Y/A, but that's all on the RB.
So I think you made some good points, but football, being the ultimate team game, makes it really hard to adequately measure what the QB "has control over".