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I'm not concerned if an absurdly impossible example "breaks" the system. Some of your examples are pretty legitimate, and should be addressed.
Believe it or not, I am not dismissing all of your points, and I do keep a careful watch each year of ways that the fantasy system seems "broken." Some specifics, though:
The QB who makes 40 completions for 300 yards is not a crappy dink-and-dunk player. In fact, if he makes 40 completions in a game, period, that means he must necessarily be producing a huge number of first downs to get that many attempts in the first place. 300+ yards per game means you'll be pushing 5000 yards and Dan Marino's passing record.
There's no particular reason to punish someone who just drives the ball downfield a little slower and more methodically. Such players are highly consistent, and they give their defenses time to rest. Drew Brees and Tom Brady exemplify this, and Peyton Manning has actually gotten more dink-and-dunk-y in his career for the reasons I just gave.
Now, I am convinced that you've actually identified some highly legitimate real-world cases that show problems with our scoring system. You might be (mostly) misidentifying the problems, though. Let's look at both example cases, starting with Albie's favorite:
Brees: 37/56 (66%) 354 yards (6.32 Y/A) and 2 TDs and 4 INTS... 28.45 fantasy points
Big Ben: 19/27 (70%) 302 yards (11.18 Y/A) and 2 TDs and 1 fumble... 28.70 fantasy points
First of all, let's try something. Let's take away all the plays on which there was a turnover, to just examine the "dink and dunk vs downfield" problem better.
Brees's line becomes 37/52 (71.1%) for 356 yards, 2 TDs. 40.45 points.
Roethlisberger remains 19/27 (70.3%) for 302 yards, 2 TDs. 31.70 points.
Quick note: they've both been penalized for 3 sacks, as well, which depresses their numbers a little bit. Note that Brees is getting roughly double points on completions, and double the penalty for incompletions. But all in all, Brees is 8-9 points ahead for only 54 yards more and a tiny bit better completion percentage, with lower yards per attempt. First, I'd put it to you that Brees's production is clearly not "lol 3 yard pass on 3rd and 6" stuff, because he's obviously moved the ball a hell of a lot. For fantasy purposes, I don't see a gigantic earth-shattering problem with him having a small advantage over Roethlisberger in fantasy. I'd agree that the advantage under the current system is too large, and I'll probably nudge the incompletion penalty a bit upward next year.
I think what you really have a problem with is Brees doing so well despite four turnovers to Big Ben's one. This is very legitimate. We've given QBs the ability to rack up huge amounts of points. Someone like Drew Brees, who is excellent, will, on the rare occasion that he throws a pick-six (only -3 points for him) will immediately get the ball back, and probably make up those -3 points in a handful of plays. That's a problem, I think.
With the Colts-Patriots game, it becomes even more clear.
Manning 38-52-396 4 TD 3 Int (rating 96,3) ~65 pts
Brady 19-25-186 2 TD 0 Int (rating 123.1) ~33 pts
Manning was legitimately more than double the QB that Brady was, in terms of "positive production." His entire stat line more than doubles Brady's.
What you obviously have a problem with is the fact that he threw 3 interceptions, and it didn't significantly dent his scoring. (It brought him down from 74 to 65. Big deal.)
TLDR: The real problem is a too-weak interception penalty. Albie is also right that attempts are probably too highly rewarded, but really, only slightly.
Believe it or not, I am not dismissing all of your points, and I do keep a careful watch each year of ways that the fantasy system seems "broken." Some specifics, though:
The QB who makes 40 completions for 300 yards is not a crappy dink-and-dunk player. In fact, if he makes 40 completions in a game, period, that means he must necessarily be producing a huge number of first downs to get that many attempts in the first place. 300+ yards per game means you'll be pushing 5000 yards and Dan Marino's passing record.
There's no particular reason to punish someone who just drives the ball downfield a little slower and more methodically. Such players are highly consistent, and they give their defenses time to rest. Drew Brees and Tom Brady exemplify this, and Peyton Manning has actually gotten more dink-and-dunk-y in his career for the reasons I just gave.
Now, I am convinced that you've actually identified some highly legitimate real-world cases that show problems with our scoring system. You might be (mostly) misidentifying the problems, though. Let's look at both example cases, starting with Albie's favorite:
Brees: 37/56 (66%) 354 yards (6.32 Y/A) and 2 TDs and 4 INTS... 28.45 fantasy points
Big Ben: 19/27 (70%) 302 yards (11.18 Y/A) and 2 TDs and 1 fumble... 28.70 fantasy points
First of all, let's try something. Let's take away all the plays on which there was a turnover, to just examine the "dink and dunk vs downfield" problem better.
Brees's line becomes 37/52 (71.1%) for 356 yards, 2 TDs. 40.45 points.
Roethlisberger remains 19/27 (70.3%) for 302 yards, 2 TDs. 31.70 points.
Quick note: they've both been penalized for 3 sacks, as well, which depresses their numbers a little bit. Note that Brees is getting roughly double points on completions, and double the penalty for incompletions. But all in all, Brees is 8-9 points ahead for only 54 yards more and a tiny bit better completion percentage, with lower yards per attempt. First, I'd put it to you that Brees's production is clearly not "lol 3 yard pass on 3rd and 6" stuff, because he's obviously moved the ball a hell of a lot. For fantasy purposes, I don't see a gigantic earth-shattering problem with him having a small advantage over Roethlisberger in fantasy. I'd agree that the advantage under the current system is too large, and I'll probably nudge the incompletion penalty a bit upward next year.
I think what you really have a problem with is Brees doing so well despite four turnovers to Big Ben's one. This is very legitimate. We've given QBs the ability to rack up huge amounts of points. Someone like Drew Brees, who is excellent, will, on the rare occasion that he throws a pick-six (only -3 points for him) will immediately get the ball back, and probably make up those -3 points in a handful of plays. That's a problem, I think.
With the Colts-Patriots game, it becomes even more clear.
Manning 38-52-396 4 TD 3 Int (rating 96,3) ~65 pts
Brady 19-25-186 2 TD 0 Int (rating 123.1) ~33 pts
Manning was legitimately more than double the QB that Brady was, in terms of "positive production." His entire stat line more than doubles Brady's.
What you obviously have a problem with is the fact that he threw 3 interceptions, and it didn't significantly dent his scoring. (It brought him down from 74 to 65. Big deal.)
TLDR: The real problem is a too-weak interception penalty. Albie is also right that attempts are probably too highly rewarded, but really, only slightly.
If Rivers has a bad day tomorrow, I could be the first place team and be 8th in total score. 
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